OPINION

BOGGS, Circuit Judge.

The Michigan Supreme Court, in a unanimous 2008 decision, held that the Detroit International Bridge Company was immune from the City of Detroit's zoning ordinances because it was a federal instrumentality for the limited purpose of facilitating commerce over the Ambassador Bridge, which connects Detroit, Michigan to Ontario, Canada. The United States was not a party to this Michigan litigation. Less than one year later, Commodities Export Company, which owned property near the Ambassador Bridge, filed suit against the City of Detroit and the United States. It alleged that the Bridge Company had unilaterally condemned roads around its property, cutting off the land and effecting a regulatory taking. It claimed that the City was liable for failing to enforce its own ordinances and demanded that the United States take a position on the Bridge Company's federal-instrumentality status and control the Bridge Company's actions. Although not originally a party, the Bridge Company eventually intervened. The United States cross-claimed against the Bridge Company, alleging that it had misappropriated the title of "federal instrumentality." The district court granted summary judgment for the United States. After the district court dismissed Commodities Export's claims, the Bridge Company appealed. For the reasons that follow, we affirm.

I

In 1921, Congress gave the Detroit International Bridge Company's predecessor, the American Transit Company, permission to build and operate what would become the Ambassador Bridge. Pub. L. No. 66-395, 41 Stat. 1439 (1921). The bridge spans the Detroit River between Detroit, Michigan and Ontario, Canada. The Bridge Company is a private, for-profit corporation, incorporated under Michigan law.

According to DIBC, the Ambassador Bridge is "the busiest commercial border crossing in North America," accounting for 26% to 30% of "all land trade between the United States and Canada." Vehicles arriving from Canada enter an enclosed compound, where federal authorities conduct border inspections. Bridge Company employees collect tolls inside of the inspection compound but must account for their presence at all times and check out with customs officials before leaving. Aside from operating the inspection compound, the federal government has no day-to-day involvement in the Bridge Company's operations. Congress did not create the Bridge Company in the first instance, and the federal government has no right to appoint members to the Bridge Company's board or otherwise control the Bridge Company's day-to-day actions.

In the mid-1990s, the Bridge Company began working with the Michigan Department of Transportation on the "Ambassador Bridge/Gateway Project." The project had two goals: (1) to facilitate easier access to the interstate-highway system from the Ambassador Bridge; and (2) to improve the Ambassador Bridge border crossing and the transportation border infrastructure network in the area of the Ambassador Bridge. The Michigan Department of Transportation took primary responsibility for the project's first objective, conducting extensive highway renovations near the bridge.

In pursuit of the second objective, the Bridge Company sought, and eventually received, federal approval to build new toll plazas, a duty-free gas station, and a weighing station for trucks. Around the year 2000, the Bridge Company asked the City of Detroit for zoning variances that would allow it to complete these projects. The City denied the requests. The Bridge Company, flouting the City's decision, went forward. The City sued. After extensive state-court litigation, the Michigan Supreme Court held that the Bridge Company was "a federal instrumentality for the limited purpose of facilitating traffic over the Ambassador Bridge." City of Detroit v. Ambassador Bridge Co., 481 Mich. 29, 748 N.W.2d 221, 223 (2008). The Bridge Company was, therefore, "immune from the zoning regulation of the city of Detroit that would preclude construction projects furthering this limited federal purpose." Ibid. A Michigan trial court entered an injunction consistent with this holding, enjoining the City from "enforcing or implementing any ordinance, regulation, policy, practice, rule or procedure the purpose or effect of which would directly inhibit the Detroit International Bridge Company ... [from] conducting its activity as a federal instrumentality." Appellant's Br. at 10. The state trial court retained jurisdiction so that it could enforce its injunction.

Less than one year after the Michigan Supreme Court's decision, Commodities Export Company filed suit against the City of Detroit and the United States. The complaint,1 in essence, alleged that the Bridge Company had effected a regulatory taking by unilaterally condemning, then closing, the only road that provided access to Commodities Export's property. According to the complaint, the City was liable because it failed to protect Commodities Export from the Bridge Company's actions. Commodities Export also argued that the United States was liable because it failed to control its instrumentality, the Bridge Company. The complaint asserted that Commodities Export was "entitled to the quiet and peaceful enjoyment of [its] property and is not required to surrender it to the Detroit International Bridge Company which Plaintiff here alleges is not a federal instrumentality," and noted that the "United States of America has yet to declare that the Detroit International Bridge Company is or is not its instrumentality." Finally, Commodities Export expressed concern that the Bridge Company's "use of its alleged status as a federal instrumentality ... [would likely] caus[e] damage to Plaintiff until or unless the Defendant United States of America takes a position on this issue and the Court issues its declaratory judgment." The complaint, therefore, sought "a mandatory injunction requiring the Defendant City of Detroit to enforce its aforesaid ordinances," and "ask[ed] [the district court] to require the Defendant United States of America to declare that the Detroit International Bridge Company is, or is not [sic] its instrumentality...."

Approximately five months after the case began, the district court set a briefing schedule and the Bridge Company then sought permission to participate as amicus curiae. The district court denied the request. More than two months later — and after Commodities Export moved for a permanent injunction and declaratory judgment — the Bridge Company sought, and ultimately received, permission to intervene as a defendant. The Bridge Company immediately filed an answer and asserted a number of affirmative defenses. It claimed that the United States was not a proper party, that the complaint did not vest the court with jurisdiction because there was no federal question, that comity, a number of abstention doctrines, and collateral estoppel counseled against the district court's entertaining the case, that the suit was the product of collusion between the City and Commodities Export, and that the court lacked personal jurisdiction over the United States.

Commodities Export filed a second amended complaint, adding the Bridge Company as a defendant and adding a number of new claims. The Bridge Company answered, re-asserting all of the affirmative defenses that it asserted in its initial answer.

The United States then filed the pleading that is relevant to this appeal — a cross-claim against the Bridge Company. It alleged that, despite the Bridge Company's contrary representations and the Michigan Supreme Court's contrary decision, the Bridge Company had "misappropriated the status of `federal instrumentality' or so-called `limited federal instrumentality.'" The Bridge Company, the United States claimed, "is not a federal instrumentality, of any kind, or any other type of arm, appendage, servant, or agent whatsoever of the United States," and thus its "representations that it is any kind of federal instrumentality are contrary to federal law." The United States, therefore, urged that the Bridge Company's "misfeasance or alleged misfeasance towards Commodities... is not properly attributable to the federal government," and sought declaratory and injunctive relief, barring the Bridge Company from claiming "that it is any kind of federal instrumentality or other arm or agent of the federal government."

On the same day, the United States also filed a motion for summary judgment on its claim as to the Bridge Company's federal-instrumentality status. It argued that the Bridge Company was not a federal instrumentality within the meaning of applicable Supreme Court and Sixth Circuit precedent and that the Michigan Supreme Court, in reaching its contrary conclusion, had misapplied federal law. The Bridge Company responded and then filed its own motion for summary judgment on the United States's cross-claim. In its summary-judgment motion, it argued that: (1) the district court lacked jurisdiction because there was no real controversy between the Bridge Company and the United States;2 (2) because Commodities Export's complaint was deficient, the United States's cross-claim should be dismissed; (3) the cross-claim was an impermissible collateral attack on the Michigan Supreme Court's holding that the Bridge Company was a federal instrumentality; and (4) the district court should abstain under either the Younger doctrine or the Rooker-Feldman doctrine.

After receiving responses from both parties and hearing oral argument, the district court denied the Bridge Company's motion and granted the motion of the United States. It reasoned, first, that there was a justiciable controversy because "in the event DIBC3 is a federal instrumentality, DIBC's actions could expose the United States to liability. Specifically, as relates to this action," the court continued, "if DIBC's actions, taken as a purported federal instrumentality, resulted in an unlawful, uncompensated taking of Plaintiff's property, the United States could be held liable to Plaintiff."4 The district court also rejected the Bridge Company's Rooker-Feldman and Younger arguments, noting that the doctrines did not apply because the United States was not a party or privy to the state-court litigation.5 Proceeding to the United States's motion, the district court held that, under binding Sixth Circuit and Supreme Court precedent, the Bridge Company did not qualify as a federal instrumentality.

After denying the Bridge Company's motion for reconsideration, the district court entered judgment in favor of the federal government and issued a declaratory judgment and permanent injunction, which provided that the Bridge Company was not a federal instrumentality, enjoined the Bridge Company "from appropriating the status of `federal instrumentality,'" and ordered the Bridge Company "to cease and desist from representing that [it is] any kind of federal instrumentality or other arm, appendage, or agency of the federal government, in state court, federal court, or elsewhere."

Just over one month later, Commodities Export moved to dismiss all of its remaining claims voluntarily, citing a confidential settlement agreement with the Bridge Company. Commodities Export's proposed order of dismissal purported to vacate the court's federal-instrumentality ruling. Both the United States and the Bridge Company filed responses. The United States objected to the supposed vacation of the court's federal-instrumentality ruling. The Bridge Company "object[ed] to Plaintiff's Motion for a voluntary dismissal of its remaining claims, for the reason that such dismissal at this stage — without more — would allow the earlier Opinions and Orders of [the district] Court to stand, all of which were entered in the absence of subject matter jurisdiction."6 The Bridge Company also argued:

The district court granted Commodities Export's motion to dismiss but expressly refused to vacate its earlier federal-instrumentality ruling, rejecting the Bridge Company's arguments as "both substantively and procedurally improper." The Bridge Company appeals.

II

At the outset, we set aside as irrelevant the Bridge Company's extensive allegations of collusion between Commodities Export and the City of Detroit. The supposedly collusive nature of Commodities Export's suit is relevant only if the alleged collusion would nullify the order that is the subject of this appeal: the district court's grant of summary judgment for the United States on the federal-instrumentality issue. It does not. It is axiomatic that "dismissal of the original suit or of a counterclaim therein for lack of subject-matter jurisdiction will require the court also to dismiss the cross-claim, unless that claim is supported by an independent basis of federal jurisdiction." 6 Charles Alan Wright & Arthur R. Miller, Federal Practice and Procedure § 1433 (3d ed. 2012) (emphasis added). Thus, if the United States's cross-claim has an independently valid jurisdictional basis, the Bridge Company's arguments about the City and Commodities Export's misconduct are wholly irrelevant.

To determine whether the district court had an independent jurisdictional basis for the cross-claim, we must address two issues: Article III's case-or-controversy requirement and statutory subject-matter jurisdiction. We consider each de novo. N. Am. Natural Res., Inc. v. Strand, 252 F.3d 808, 812 (6th Cir.2001) (case or controversy); Williams v. Duke Energy Int'l., Inc., 681 F.3d 788, 798 (6th Cir.2012) (statutory subject-matter jurisdiction).

Under Article III, the federal courts may exercise jurisdiction only if the parties have presented a live case or controversy. U.S. Const. art. III, § 2. We have no power to offer an advisory opinion, based on hypothetical facts. Fialka-Feldman v. Oakland Univ. Bd. of Trustees, 639 F.3d 711, 715 (6th Cir.2011). Where, as here, a party seeks declaratory relief, "[t]he difference between an abstract question and a `controversy' ... is necessarily one of degree." Golden v. Zwickler, 394 U.S. 103, 108, 89 S.Ct. 956, 22 L.Ed.2d 113 (1969) (internal quotation marks omitted). Thus, when we face the "difficult task of distinguishing between actual controversies and attempts to obtain advisory opinions on the basis of hypothetical controversies," Coal. for Gov't Procurement v. Fed. Prison Indus., Inc., 365 F.3d 435, 458 (6th Cir.2004) (internal quotation marks omitted), we ask "whether the facts alleged, under all the circumstances, show that there is a substantial controversy, between parties having adverse legal interests, of sufficient immediacy and reality to warrant the issuance of a declaratory judgment." Golden, 394 U.S. at 108, 89 S.Ct. 956 (internal quotation marks omitted).

The United States easily clears this hurdle. Commodities Export haled the federal government into court, on the strength of a number of cases holding the United States liable for the wrongs of its instrumentalities. See Slattery v. United States, 635 F.3d 1298, 1307 (Fed.Cir.2011) (en banc) (collecting cases upholding Tucker Act Jurisdiction, and thus the possibility of the United States being liable, for entities not supported by appropriated funds); L'Enfant Plaza Props., Inc. v. United States, 209 Ct.Cl. 727, 727-28 (1976); Breitbeck v. United States, 500 F.2d 556, 558-60 (Ct.Cl.1974), abrogated on other grounds by Slattery, 635 F.3d at 1321; see also Lebron v. Nat'l R.R. Passenger Corp., 513 U.S. 374, 400, 115 S.Ct. 961, 130 L.Ed.2d 902 (1995) (holding that Amtrak, which operated as a private company, was part of the government for First Amendment purposes). The federal government, therefore, faced the prospect of having to pay Commodities Export for the Bridge Company's alleged misdeeds, were the Bridge Company a federal instrumentality. And even if the court determined that the Bridge Company had done no wrong, the federal government still would have — indeed already has — incurred the litigation costs of entering an appearance and defending against the suit. Further, the record indicates that the Bridge Company claimed federal-instrumentality status elsewhere, potentially triggering federal-government liability and litigation costs in other proceedings. The Bridge Company's holding itself out as a federal instrumentality, limited or otherwise, therefore presented "a substantial controversy ... [between the Bridge Company and the United States, which was] of sufficient immediacy and reality to warrant the issuance of a declaratory judgment." Golden, 394 U.S. at 108, 89 S.Ct. 956 (internal quotation marks omitted).

Of course, the existence of an Article III case or controversy is not itself enough to open the federal courthouse door. The plaintiff must also show that the court has subject-matter jurisdiction under a relevant statute. Here, the statutory-subject-matter-jurisdiction inquiry is simple, because "the district courts shall have original jurisdiction of all civil actions, suits or proceedings commenced by the United States." 28 U.S.C. § 1345. The United States brought this suit against the Bridge Company as soon as the Bridge Company intervened. The district court had the power to entertain the claim under § 1345.

The district court, therefore, had jurisdiction over the United States's cross-claim. Accordingly, even if Appellants were correct that the original suit was a product of collusion between the City and Commodities Export, in which the federal government somehow cooperated, the United States's suit against the Bridge Company could proceed.

III

After jurisdiction, but before the merits, we must decide what impact, if any, the Michigan Supreme Court's federal-instrumentality decision has on subsequent federal-court litigation by the United States, a party not involved in the state-court action. The possible resolutions are: (1) the Michigan Supreme Court decision binds the federal courts because it is really a decision on state law; (2) because the state trial court retained jurisdiction to enforce its injunction, the Anti-Injunction Act bars the district court from enjoining the Bridge Company's assertion of its federal-instrumentality status; (3) the federal courts should extend the abstention doctrine announced in Railroad Commission v. Pullman Co., 312 U.S. 496, 61 S.Ct. 643, 85 L.Ed. 971 (1941), treat the state-court injunction like a state statute, and allow the state to enforce its decision; and (4) none of the above — a state supreme court's interpretation of federal law receives no special deference from the federal courts, as long as no preclusion doctrine bars us from considering the issue with fresh eyes.

The first of these options, which the Bridge Company pressed vigorously at oral argument, is simply wrong. Without doubt, we defer to a state-court interpretation of state law. Republic Bank & Trust Co. v. Bear Stearns & Co., Inc., 683 F.3d 239, 247 (6th Cir.2012) (acknowledging that on a "matter of substantive state law ... we must defer to the state courts"). But that principle does not control here. The Michigan Supreme Court's decision in City of Detroit dealt with an issue "of federal genesis," United States v. Miami Univ., 294 F.3d 797, 811 (6th Cir.2002): whether the Bridge Company qualified as an instrumentality of the federal government. An affirmative answer — under federal law — means liability for the federal government. Furthermore, the Michigan Supreme Court's analysis of the federal-instrumentality issue rested almost entirely on federal precedent and principles of federal preclusion. See City of Detroit, 748 N.W.2d at 224-33.

It is true that the effect of the Michigan Supreme Court's holding was to prevent a city from enforcing its own zoning ordinance. But the only reason for that outcome was the Michigan Supreme Court's belief that "under both the test in United States v. Michigan[, 851 F.2d 803, 806 (6th Cir.1988)] and the conduct-based test in Name.Space [v. Network Solutions, Inc., 202 F.3d 573, 581-82 (2d Cir.2000)], the trial court correctly concluded that the DIBC is an instrumentality of the federal government." City of Detroit, 748 N.W.2d at 230 (citing two federal cases enunciating federal law). Substantive principles of Michigan law, in other words, played no significant role in the court's analysis.

It is also true that no federal statute confirms or denies that the Bridge Company is a federal instrumentality. But this does not mean that the Michigan Supreme Court's decision is a matter of state law. Where "it is plain that the problems involved are uniquely federal in nature," Banco Nacional de Cuba v. Sabbatino, 376 U.S. 398, 424, 84 S.Ct. 923, 11 L.Ed.2d 804 (1964), we have "authority ... to formulate what has come to be known as `federal common law.'" Texas Indus., Inc. v. Radcliff Materials, Inc., 451 U.S. 630, 640, 101 S.Ct. 2061, 68 L.Ed.2d 500 (1981). Our power to do so, of course, is narrowly circumscribed. See id. at 641, 101 S.Ct. 2061. But "such ... areas as those concerned with the rights and obligations of the United States" are prime arenas for the exercise of federal-common-law authority. Ibid. (citing United States v. Little Lake Misere Land Co., 412 U.S. 580, 93 S.Ct. 2389, 37 L.Ed.2d 187 (1973); Clearfield Trust Co. v. United States, 318 U.S. 363, 63 S.Ct. 573, 87 L.Ed. 838 (1943)). The Bridge Company's federal-instrumentality status is just such a question. Whether the Bridge Company is so intimately involved with the federal government that it qualifies as a federal instrumentality, and thus makes the United States answerable for its actions, is a "uniquely federal" question. Banco Nacional de Cuba, 376 U.S. at 424, 84 S.Ct. 923. Federal-instrumentality status of any kind, limited or not, is a federal-common-law issue, not a question of state law.

The second option, barring the United States's suit under the Anti-Injunction Act, fares no better. Under the Anti-Injunction Act, "[a] court of the United States may not grant an injunction to stay proceedings in a State court except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments." 28 U.S.C. § 2283. The Act, however, does not bar litigation by parties that were "strangers to the state court proceedings" Gottfried v. Med. Planning Servs., Inc., 142 F.3d 326, 329 (6th Cir. 1998) (quoting Cnty. of Imperial, Cal. v. Munoz, 449 U.S. 54, 59-60, 101 S.Ct. 289, 66 L.Ed.2d 258 (1980)) (internal quotation marks omitted); see also Hale v. Bimco Trading Inc., 306 U.S. 375, 377-78, 59 S.Ct. 526, 83 L.Ed. 771 (1939). Because the United States was not a party to the state-court litigation, the Anti-Injunction Act does not apply.

Nor does Gottfried, 142 F.3d at 330-33 (extending Pullman abstention, the third option), counsel a different conclusion. There, a panel of our court held that "equity, comity, and our federalist judicial system require the federal court to give the state judge the first chance to bring [an earlier] injunction into compliance with constitutional law." Id. at 330. Gottfried, though, was a federal constitutional attack on a state injunction, which enforced state law. Here, in contrast, we deal only with a federal claim that could, hypothetically, have an impact on a state-court injunction in some future, not-yet-filed litigation and which turns on an issue of federal common law. The difference is stark. Setting equity aside,7 comity and our federal system favor a federal merits decision. Comity generally refers to the respect that we accord a state court. But comity is a two-way street. Just as we could not bind the Michigan Supreme Court on a point of Michigan law, so too may we consider afresh a federal issue that the Michigan Supreme Court has decided, so long as some other preclusion or abstention doctrine does not bar our review. This result promotes the smooth operation of "our federalist judicial system," because it gives the state and federal courts each the final say over the law that they are best suited, respectively, to apply. Ibid.

That leaves the fourth and final option, which is also the correct option: none of the above. We have explained that "a state court's opinion on an issue of federal law ... is entitled to no deference whatsoever." First Am. Title Co. v. Devaugh, 480 F.3d 438, 455 (6th Cir.2007). And of course, "[n]otions of federalism do not require this court to follow a state court's holdings with respect to federal questions." Kuhnle Brothers, Inc. v. Cnty. of Geauga, 103 F.3d 516, 520 (6th Cir. 1997). Thus, absent applicable abstention or preclusion doctrines, of which there are none in this case,8 the Michigan Supreme Court's decision is at most non-binding, persuasive authority, which we are free to follow or to reject, depending on our interpretation of our federal law.

IV

Our only remaining task is to determine whether the district court's grant of summary judgment to the United States on the federal-instrumentality issue was proper. We review the grant of summary judgment de novo, taking all facts and drawing all reasonable inferences in the non-moving party's favor. ACLU of Ky. v. Mercer Cnty., Ky., 432 F.3d 624, 628 (6th Cir.2005). Summary judgment is appropriate where "the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law." Fed.R.Civ.P. 56(a).

The usual federal-instrumentality case assesses whether a company either chartered by, or intimately involved with, the federal government is exempt from state taxation. The progenitor of today's federal-instrumentality doctrine is McCulloch v. Maryland, 17 U.S. (4 Wheat.) 316, 425-37, 4 L.Ed. 579 (1819), which held that the Second Bank of the United States was exempt from a Maryland tax. Over time, the Supreme Court has treated various entities as instrumentalities of the federal government: federal land banks, see, e.g., Fed. Land Bank of St. Paul v. Bismarck Lumber Co., 314 U.S. 95, 62 S.Ct. 1, 86 L.Ed. 65 (1941); Fed. Land Bank of Wichita v. Bd. of Cnty. Comm'rs, 368 U.S. 146, 82 S.Ct. 282, 7 L.Ed.2d 199 (1961); a corporation chartered solely to provide lumber for World War I fighter planes, Clallam Cnty., Wash. v. United States, 263 U.S. 341, 44 S.Ct. 121, 68 L.Ed. 328 (1923); the Red Cross, Dep't of Emp't v. United States, 385 U.S. 355, 87 S.Ct. 464, 17 L.Ed.2d 414 (1966); and Amtrak, Lebron v. Nat'l R.R. Passenger Corp., 513 U.S. 374, 115 S.Ct. 961, 130 L.Ed.2d 902 (1995).

Although the federal-instrumentality doctrine has existed, in one form or another, for nearly two hundred years, "there is no simple test for ascertaining whether an institution is so closely related to governmental activity as to become a tax-immune instrumentality." Dep't of Emp't, 385 U.S. at 358-59, 87 S.Ct. 464. "[T]he Supreme Court has looked to several factors, including: whether the entity was created by the government; whether it was established to pursue governmental objectives; whether government officials handle and control its operations; and whether the officers of the entity are appointed by the government." Augustine v. Dep't of Veterans Affairs, 429 F.3d 1334, 1339 n. 3 (Fed.Cir.2005) (citing Lebron, 513 U.S. at 397-98, 115 S.Ct. 961). We summarized these factors in Michigan, 851 F.2d at 806, as "the purpose for which [the alleged instrumentality was] created,... whether [it] continue[s] to perform that function, and ... the federal government's control over and involvement with the[] organization[]."

But however one approaches the analysis, the Bridge Company bears none of the hallmarks of a federal instrumentality. It is a private, for-profit corporation, created by private individuals, not by the United States. Cf. Lebron, 513 U.S. at 383, 115 S.Ct. 961 ("Congress established Amtrak in order to avert the threatened extinction of passenger trains in the United States." (emphasis added)). Although it received a charter from Congress, entitling it to build and operate the Ambassador Bridge, the Bridge Company's Articles of Incorporation recite that it "is organized to engage in any activity within the purposes for which corporations may be organized under the Business Corporation Act of Michigan." Cf. Clallam Cnty., 263 U.S. at 343, 44 S.Ct. 121 (noting that corporation was formed under Congressional authorization to Director of Aircraft Production "to form one or more corporations under the laws of any state for the purchase, production, manufacture and sale of aircraft, or equipment or materials therefor ... whenever in his judgment it would facilitate the production of aircraft ... for the United States and Governments allied with it `in the prosecution of the present war.'"). The government, moreover, does not control the Bridge Company's day-to-day operations. Cf. id. at 344, 44 S.Ct. 121 (noting that lumber-production company was "used by [the United States] solely"). Nor does it have the power to appoint Bridge Company directors. Cf. Lebron, 513 U.S. at 385, 115 S.Ct. 961 (noting that President of United States directly appoints six of nine directors); Dep't of Emp't, 385 U.S. at 359, 87 S.Ct. 464 (describing President's power to appoint head of organization and additional governors). Nor does it even have a significant financial stake in the Bridge Company's success. Cf. Clallam Cnty., 263 U.S. at 343, 44 S.Ct. 121 (noting that United States subscribed to almost all of corporation's stock and purchased all of the bonds that the corporation issued). Further, the Bridge Company works near, not on behalf of, the federal agencies that perform federal functions at the border. Bridge Company employees do collect tolls inside the federal government's inspection compound, but they must account for their presence at all times and check out with customs officials before leaving. The Bridge Company, moreover, is a frequent adversary of the United States in litigation, and the Supreme Court has twice held that the Bridge Company is not immune from state taxation, which, of course, it would be if it were a federal instrumentality. See Detroit Int'l Bridge Co. v. Corp. Tax Appeal Bd., 294 U.S. 83, 85-86, 55 S.Ct. 332, 79 L.Ed. 777 (1935) (holding that state government could tax Bridge Company); Detroit Int'l Bridge Co. v. Corp. Tax Appeal Bd., 287 U.S. 295, 297-98, 53 S.Ct. 137, 77 L.Ed. 314 (1932) (same).

It is true that the Bridge Company received authorization from Congress to build and operate the Ambassador Bridge, and thus plays a role in facilitating international commerce. But that, without more, does not make the Bridge Company a federal instrumentality, for it would be "extravagant to say that an independent private corporation for gain, created by a state, is exempt from state taxation [as a federal instrumentality] ... because it is employed by the United States, even if the work for which it is employed is important and takes much of its time." Baltimore Shipbuilding & Dry Dock Co. of Baltimore City v. Mayor and City Council of Baltimore, 195 U.S. 375, 382, 25 S.Ct. 50, 49 L.Ed. 242 (1904) (Holmes, J.); see also Fidelity & Deposit Co. of Md. v. Penn., 240 U.S. 319, 323, 36 S.Ct. 298, 60 L.Ed. 664 (1916) ("[M]ere contracts between private corporations and the United States do not necessarily render the former essential government agencies, and confer freedom from state control."). Indeed, the federal agencies charged with border protection perform the truly federal functions in the inspection compound, which the Bridge Company does not control. Nor does the Bridge Company's ability to issue private bonds, its cooperation with the Michigan Department of Transportation, or its participation in a federally-sponsored effort to reduce border-crossing times suggest that it is an instrumentality of the federal government. The Bridge Company, instead, is a for-profit corporation that makes its money by facilitating international commerce, an activity that has some relationship to the United States's legitimate governmental powers. It is not "so closely related to governmental activity as to become... [an] instrumentality." Dep't of Emp't, 385 U.S. at 385-59, 87 S.Ct. 464. The district court correctly granted summary judgment for the United States.

V

The Bridge Company's last argument is that the district court should not have allowed Commodities Export to dismiss its claims voluntarily, unless the district court also vacated its earlier summary-judgment decision for the United States. Federal Rule of Civil Procedure 41(a)(2) allows a district court to "dismiss[]... [an action], on terms that the court considers proper." "The district court's decision regarding the Rule 41(a)(2) motion is reviewed for abuse of discretion." Eagles, Ltd. v. Am. Eagle Found., 356 F.3d 724, 730 (6th Cir.2004).

The district court first noted that federal courts "commonly grant Rule 41 motions and dismiss individual claims after, in previous orders, other claims have been dismissed, settled, or otherwise resolved." (citing Montgomery v. Honda of Am. Mfg., Inc., 47 Fed.Appx. 342, 345 (6th Cir.2002)). Further, the resolution of the cross-claim — which had an independent jurisdictional basis — was not dependent on the resolution of Commodities Export's claim. The same principle that renders irrelevant the validity of Commodities Export's complaint also vitiates the Bridge Company's Rule 41 claim. 6 Charles Alan Wright & Arthur R. Miller, Federal Practice and Procedure § 1433. Thus, the district court did not abuse its discretion in granting Commodities Export's Rule 41 motion.

VI

In sum, the federal courts have jurisdiction over the United States's cross-claim, the action that underlies this appeal. We owe no deference to the Michigan Supreme Court's interpretation of federal common law. On the merits, the district court correctly held that the Bridge Company is not a federal instrumentality. And it was not error to grant Commodities Export's voluntary dismissal motion without vacating the grant of summary judgment for the United States. We AFFIRM the district court's judgment and injunction.