HAYNES, Circuit Judge:

The principal question before the district court was whether the employers' pension benefit plan in this case is a "governmental plan" within the meaning of section 3(32) the Employee Retirement Income Security Act of 1974 ("ERISA"), 29 U.S.C. § 1002(32). The Plaintiffs-Appellants (the "Plaintiffs," collectively) are approximately forty former employees of New Orleans Public Service, Inc. and retirees of Transit Management of Southeast Louisiana, Inc. They filed suit claiming denial of medical insurance, Medicare premiums, and deductible reimbursements. The district court held that the pension benefit plan was a "governmental plan" exempt from ERISA and granted RTA and TMSEL's (the "Defendants," collectively) motion to dismiss for lack of subject matter jurisdiction. Because we conclude that the district court employed the wrong procedural mechanism for analyzing this case, we vacate the judgment and remand this case to the district court.

I.

Prior to 1983, the New Orleans transit system was operated by New Orleans Public Service, Inc. ("NOPSI"), a private company. In the late 1970s and early 1980s, the system converted to a publicly held system, owned by the Regional Transit Authority ("RTA") and operated by Transit Management of Southeast Louisiana, Inc. ("TMSEL"). As a result of the change in ownership and management, all employees of NOPSI became employees of TMSEL. At the time the RTA purchased the transit system, NOPSI, the transit union, and the City of New Orleans had a preexisting agreement pursuant to the Urban Mass Transportation Act of 1964, which provided for "fair and equitable arrangements" for employee benefits. In March 1983, the RTA and TMSEL, as successors to NOPSI, agreed that they would continue to provide the same benefits employees enjoyed under the preexisting agreement.

In June 1983, the RTA completed the purchase of the transit system from NOPSI. At the same time, the RTA, TMSEL, and NOPSI entered into an additional agreement, "The Employee and Retiree Pension and Welfare Benefit Agreement" (the "Benefit Agreement") which specifically recognized the RTA and TMSEL's benefit obligations. The RTA became the sponsor of the Plan, and TMSEL became the administrator. The Benefit Agreement provided that each employee transferred from NOPSI to the RTA or TMSEL would continue to receive the same coverage and benefit levels they received as an employee of NOPSI. The Benefit Agreement also made the RTA and TMSEL responsible for making any payments due for any benefits of the former NOPSI employees, and established a funding structure to ensure that the pension benefits were maintainable.

At the time of the purchase and agreements, the RTA was considered a public entity — a "political subdivision" of the state of Louisiana1 — and TMSEL was a privately owned corporation, created in 1983 by an agreement between the RTA and ATE Management and Service Company to operate the transit system. In 2004, the Louisiana State Legislature designated TMSEL as a political subdivision for litigation purposes. See LA.REV.STAT. ANN. § 13:5102. In 2009, TMSEL ceased operations and no longer provided services to the RTA. From 2009-12, the public transportation was instead operated by a separate private corporation.2 In 2012, the RTA became 100% owner of TMSEL.

The Plaintiffs are retired former employees of NOPSI and/or TMSEL. According to the Plaintiffs, from the system's private-to-public conversion in 1983 until March 2006, the RTA administered the Employee Benefit Plan ("the Plan") consistent with the Benefit Agreement: it provided premium-free medical insurance, life insurance, supplemental Medicare payments, and reimbursed Medicare premiums. However, the Plaintiffs allege that, in March 2006, the RTA and/or TMSEL stopped providing Medicare premiums and deductible reimbursements to retirees and began charging premiums for medical insurance. The Plaintiffs aver they were originally told the changes were temporary, but that they have continued until the present day.

In December 2012, the Plaintiffs filed suit against the RTA as plan sponsor under § 1002(16)(B), and TMSEL as plan administrator under § 1002(16)(A), alleging that the Defendants violated ERISA when they implemented the changes to the benefit plan. The Plaintiffs sought to collect the same welfare benefits they had received from NOPSI. The complaint alleges that the RTA and/or TMSEL wrongfully denied ERISA welfare and retirement benefits in violation of 29 U.S.C. § 1132(a)(1)(B), and that the RTA and/or TMSEL breached their fiduciary duties under ERISA in violation of § 1132(a)(2). The Defendants filed a motion to dismiss the complaint for lack of subject matter jurisdiction under Federal Rule of Civil Procedure 12(b)(1). The Defendants asserted that the benefit plan fell within the "governmental plan" exemption to ERISA, and that ERISA provided the only basis for subject matter jurisdiction.3 See 29 U.S.C. § 1003(b)(1) ("The provisions of [the coverage] subchapter shall not apply to any employee benefit plan if such plan is a governmental plan."). The district court granted the Defendants' motion. The Plaintiffs appealed.

II.

We have previously suggested that the "governmental plan" exemption implicates our subject matter jurisdiction such that claims concerning such a plan should be dismissed under Rule 12(b)(1). Shirley v. Maxicare Tex., Inc., 921 F.2d 565, 567 (5th Cir.1991). In Shirley, we held that because a benefits plan was a "governmental plan" exempt from ERISA's requirements, the district court lacked jurisdiction to order arbitration. Id. at 566-67 (citing § 1003(b)). However, more recent developments in Supreme Court case law and our en banc decision in ACS Recovery Services, Inc. v. Griffin, 723 F.3d 518 (5th Cir.2013) (en banc), cert denied, ___ U.S. ___, 134 S.Ct. 618, 187 L.Ed.2d 400 (2013), make Shirley inapplicable to our decision today.

The Supreme Court has repeatedly instructed that we must avoid conflating the question of whether we have subject matter jurisdiction to consider a claim with the determination of whether the plaintiff has stated a valid claim for relief. See Arbaugh v. Y & H Corp., 546 U.S. 500, 510-11, 126 S.Ct. 1235, 163 L.Ed.2d 1097 (2006); see also Reed Elsevier, Inc. v. Muchnick, 559 U.S. 154, 160-61, 130 S.Ct. 1237, 176 L.Ed.2d 18 (2010) (explaining that the word "jurisdiction" refers to a court's adjudicatory authority and therefore only properly applies to specific delineations of that authority). For instance, the Court in Arbaugh rejected the argument that proving a defendant is an "employer" for purposes of Title VII was necessary to establish subject matter jurisdiction. Arbaugh, 546 U.S. at 508, 514-16, 126 S.Ct. 1235. In so concluding, the Court applied a "readily administrable bright line" standard for determining whether a statute's provision is an element of a plaintiff's claim for relief or a jurisdictional requirement. Id. This standard turns on whether Congress has specifically designated a statutory limitation on coverage as jurisdictional. Id. at 516, 126 S.Ct. 1235 ("[W]hen Congress does not rank a statutory limitation on coverage as jurisdictional, courts should treat the restriction as nonjurisdictional in character."). Applying this standard, the Court focused primarily on the definition of "employer" in 42 U.S.C. § 2000e(b), explaining that the statute's text did not "clearly stat[e]" that the defendant must fall within the definition of "employer" in order for there to be federal jurisdiction to consider the claim. Arbaugh, 546 U.S. at 515, 126 S.Ct. 1235. The Court also observed that the definition of "employer" was not located in Title VII's jurisdictional provision, but rather "appeared in a separate provision that does not speak in jurisdictional terms or refer in any way to the jurisdiction of the district courts." Id. (citation and internal quotation marks omitted).

Later in Reed Elsevier, the Court reiterated the importance of "using the term `jurisdictional' only when it is apposite." 559 U.S. at 161, 130 S.Ct. 1237. The Court held that the Copyright Act's requirement that holders register their works before suing for copyright infringement was not a jurisdictional limitation, in part because the registration requirement does not "clearly state[]" that it is jurisdictional and therefore should not be treated as such. Id. at 163-66, 130 S.Ct. 1237; see also 17 U.S.C. § 411(a).

In accord with the Court's direction, last year in Griffin we rejected our prior precedent that a failure to state a valid claim for equitable relief under ERISA deprived the court of subject matter jurisdiction. 723 F.3d at 522-23 (citing Steel Co. v. Citizens for a Better Env't, 523 U.S. 83, 89, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998) ("Dismissal for lack of subject-matter jurisdiction because of the inadequacy of the federal claim is proper only when the claim is so insubstantial, implausible, foreclosed by prior decisions of [the Supreme Court], or otherwise completely devoid of merit as not to involve a federal controversy." (citation and internal quotation marks omitted))). We noted that whether a party has a valid claim does not implicate subject matter jurisdiction. Griffin, 723 F.3d at 523 ("[W]hether a claim for equitable relief under ERISA § 502(a)(3) has been stated is within federal courts' jurisdiction irrespective of the claim's ultimate merit."). In so concluding, we effectively overruled our contrary precedent.4 Compare Griffin, 723 F.3d at 523, with Tinoco v. Marine Chartering Co., Inc., 311 F.3d 617, 623 (5th Cir.2002) ("Where federal subject matter jurisdiction is based on ERISA, but the evidence fails to establish the existence of an ERISA plan, the claim must be dismissed for lack of subject matter jurisdiction." (citation and internal quotation marks omitted)), abrogated by Griffin, 723 F.3d at 523. Our holding in Griffin employed exactly the kind of reasoning called for by the Supreme Court in Arbaugh and Reed Elsevier which has led at least five of our sister circuits to reject the notion that the actual existence (as opposed to the allegation) of a plan covered by ERISA is a jurisdictional prerequisite.5

Here, the Plaintiffs filed suit seeking relief under ERISA and arguing that the Plan in question is governed by ERISA. The Defendants responded in the district court and before our court that federal jurisdiction is lacking because the Plan falls within ERISA's "governmental plan" exemption. See § 1003(b)(1). However, nothing in § 1003(b)(1) "clearly states" that the "governmental plan" exemption is a jurisdictional limitation, nor is this exemption listed in ERISA's jurisdictional provision — 29 U.S.C. § 1132(e). See Reed Elsevier, 559 U.S. at 163, 130 S.Ct. 1237; Arbaugh, 546 U.S. at 515, 126 S.Ct. 1235. Therefore, unless the Plaintiffs' claim is "so insubstantial [or] implausible... as not to involve a federal controversy," the Plaintiffs' pleading triggers federal jurisdiction. See Griffin, 723 F.3d at 523 (citations and internal quotation marks omitted). This commonsense approach espoused by Griffin to the jurisdictional issue presented governs this case such that any contrary reading of Shirley cannot stand.6

Of course, once it is determined (through a Rule 12(b)(6) or 56 motion or a trial on the merits) that the plan at issue is a "governmental plan," then ERISA does not provide relief or remedies, and that claim must be dismissed. See § 1003(b)(1) ("The provisions of this subchapter shall not apply to any employee benefit plan if... such plan is a governmental plan."). However, that is different from stating that a district court lacks jurisdiction over a case where one party contends Plan A is an ERISA plan and the other party contends that Plan A is a "governmental plan" (or otherwise is not an ERISA plan). See Steel, 523 U.S. at 89, 118 S.Ct. 1003 ("[T]he absence of a valid (as opposed to arguable) cause of action does not implicate subject-matter jurisdiction, i.e., the courts' statutory or constitutional power to adjudicate the case."); see, e.g., Daniels-Hall v. Nat'l Educ. Ass'n, 629 F.3d 992, 997 (9th Cir. 2010) ("[T]o ask whether the alleged Plan is subject to ERISA is a merits question.").7

Accordingly, because a federal district court has jurisdiction to decide whether or not a plan is an ERISA plan as claimed by the plaintiff in the complaint, we conclude that, under Supreme Court precedent and Griffin, the proper procedural vehicle to raise the question of whether a purported ERISA plan is a "governmental plan" is either Rule 12(b)(6) or, if factual information outside the pleadings is needed, Rule 56 (if factual issues cannot be resolved then, of course, a trial may be needed). The question then becomes whether this procedural distinction makes a difference here. Cf. Daniels-Hall, 629 F.3d at 998 (no difference in the outcome between the two procedures). We conclude that it does.

"A case is properly dismissed for lack of subject matter jurisdiction when the court lacks the statutory or constitutional power to adjudicate the case." Krim v. pcOrder.com, Inc., 402 F.3d 489, 494 (5th Cir.2005) (citation and internal quotation marks omitted). In considering a challenge to subject matter jurisdiction, the district court is "free to weigh the evidence and resolve factual disputes in order to satisfy itself that it has the power to hear the case." Id. (citation and internal quotation marks omitted). Thus, under Rule 12(b)(1), the district court can resolve disputed issues of fact to the extent necessary to determine jurisdiction; by contrast, disputed questions of fact are anathema to Rule 12(b)(6) jurisprudence, unless those disputed facts are immaterial to the outcome. Compare Montez v. Dep't of Navy, 392 F.3d 147, 149 (5th Cir.2004) ("In general, where subject matter jurisdiction is being challenged, the trial court is free to weigh the evidence and resolve factual disputes in order to satisfy itself that it has the power to hear the case."), with In re Katrina Canal Breaches Litig., 495 F.3d 191, 205 (5th Cir.2007) (When deciding a Rule 12(b)(6) motion, "[t]he court accepts all well-pleaded facts as true, viewing them in the light most favorable to the plaintiff." (citation and internal quotation marks omitted)). In light of the complexity of the facts here involved, this case cannot be resolved without some resort to "the facts." As such, because the procedural mechanism employed could very well affect the outcome, the matter should be directed to the district court in the first instance.8

Accordingly, we VACATE the district court's order in its entirety and remand for reconsideration under a proper procedural vehicle. As a result, we do not reach the merits of the "governmental plan" argument or the timing question beyond noting that, typically, facts are assessed at the time the cause of action arose. See, e.g., Hightower v. Tex. Hosp. Ass'n, 65 F.3d 443, 447 (5th Cir.1995) (deciding whether a benefit plan was a "governmental plan" at the time it was terminated and members of the plan were denied payments from the resulting surplus of funds).

VACATED and REMANDED.