POSNER, Circuit Judge.

Before us are consolidated appeals in a pair of diversity suits governed, the parties agree, by Indiana law. One suit pits two insurance companies, National Union and Lexington (both subsidiaries of American International Group), against Mead Johnson, which purchased liability coverage from them. The other suit is just between National Union and Mead Johnson. We can ignore the procedural tangle reflected in the caption.

Mead Johnson had purchased a primary Commercial General Liability policy (a standard policy issued by many insurance companies) from National Union. The policy has a limit of $2 million for liability for what is called "personal and advertising injury." Mead also has an excess liability policy from Lexington (a policy that kicks in when an insured's liability exceeds the limit in his primary policy) that has a limit of $25 million. The insurance companies sought and obtained (on motions for summary judgment) declaratory judgments that they have no duty to pay claims that Mead Johnson filed with them regarding two tort suits against it. So Mead has appealed.

A recent spinoff from Bristol-Myers Squibb, Mead Johnson is virtually a one-product company. That product is the upscale infant formula Enfamil. See "Enfamil," Wikipedia, http://en.wikipedia.org/ wiki/Enfamil (visited Oct. 24, 2013). It is sold worldwide, and is alleged to have accounted for 60 percent of Mead Johnson's $2.88 billion earnings in 2008 on the eve of the tort suits that have given rise to these appeals. The tort suits are a reflection of Mead's efforts to maintain its dominance of the global baby-formula market, efforts that have resulted in repeated legal skirmishes with a major competitor, PBM Products, LLC (part of a much larger company, Perrigo). In two earlier suits, both settled, PBM had sued Mead for false advertising. PBM Products, Inc. v. Mead Johnson & Co., 03:01-cv-199 (E.D.Va. 2001); PBM Products, Inc. v. Mead Johnson & Co., 03:02-cv-944 (E.D.Va.2002). Turning the tables on its opponent, Mead had sued PBM for trade dress infringement. Mead Johnson & Co. v. PBM Nutritionals, LLC, 1:06-cv-1246 (S.D.Ind. 2006). That case was settled too.

The insurance suits that the current appeals bring before us arose out of PBM's third lawsuit against Mead (again for false advertising), plus a class action suit against Mead for consumer fraud. PBM's suit, filed in 2009, eventuated in a jury award of $13.5 million, affirmed in PBM Products, LLC v. Mead Johnson & Co., 639 F.3d 111, 128 (4th Cir.2011). Mead wants its insurers to pay that judgment, plus the $15 million settlement that it made to resolve the class action suit.

PBM's suit claimed that Mead had falsely asserted that PBM's less expensive infant formula (a "store brand"—that is, a generic rather than a branded product, to which the retail outlet that sells it attaches its own brand name) lacked two key fats that promote brain and eye development. Filed in April 2009, the suit sought some $500 million in damages for product disparagement, a tort that the insurance policies that Mead Johnson had bought from National Union and Lexington expressly cover as a form of "advertising injury." But Mead did not notify National Union or Lexington of the suit until December 2009—by which time the trial in PBM's suit had ended in the $13.5 million verdict against Mead. (Why Mead Johnson didn't notify its insurers about the PBM suit until losing at the trial is the abiding mystery of this case. At oral argument we asked Mead Johnson's counsel why, and he said he didn't know. We find this hard to believe, but are left in the dark.)

Both insurance policies required Mead to notify the insurance companies "as soon as practicable." The National Union policy required notice of any occurrence or claim as soon as practicable after the occurrence or claim. The Lexington policy, being an excess policy, required notice only of a claim or suit, and only if the claim or suit was "reasonably likely" to trigger coverage on the "assumption that an Insured is liable for the damages claimed," namely damages of more than $2 million, the limit of National Union's policy.

These are important provisions. If a claim against an insured is covered by the insurance policy, the insurer has a vital interest in supervising the defense against the claim, for its money is riding on the outcome. And so the policies entitle the insurers to control the insured's defense against a covered claim and negotiate a settlement. But this is subject to their fiduciary duty to the insured: the insurer is forbidden to "sell out" an insured, for example by settling for the policy limit without making a reasonable effort to reduce the insured's liability above that limit. Lockwood Int'l, B.V. v. Volm Bag Co., 273 F.3d 741, 744-46 (7th Cir.2001); see also Erie Ins. Co. v. Hickman by Smith, 622 N.E.2d 515, 518-19 (Ind.1993); Economy Fire & Casualty Co. v. Collins, 643 N.E.2d 382, 385-86 (Ind.App.1994); Schwartz v. Liberty Mutual Ins. Co., 539 F.3d 135, 142 (2d Cir.2008); Venn v. St. Paul Fire & Marine Ins. Co., 99 F.3d 1058, 1064-65 (11th Cir.1996).

National Union's policy has separate notice provisions for an occurrence, defined as "an accident" ("an unexpected happening without an intention or design," Auto-Owners Ins. Co. v. Harvey, 842 N.E.2d 1279, 1283 (Ind.2006)) and for a claim or suit against the insured. An amendment (called an "endorsement") to the policy provided that the insured would not be deemed to have "knowledge" of an occurrence until the insured's "Director of Risk Management" received notice of the occurrence, so only then would the clock start running on notifying the insurer. Mead Johnson claims that its Director of Risk Management did not learn of the $500 million suit by PBM until the trial ended, days before Mead notified the insurers. We find this hard to believe. This was the fourth recent suit between the companies. Even to a company the size of Mead Johnson, $500 million is a lot of money, though doubtless an extravagant estimate of PBM's actual damages; the jury's award of damages to PBM was, after all, only 2.7 percent of $500 million.

It is understandable why an insured would not want its duty of notifying its insurers to kick in whenever there was an occurrence, which might well be trivial (baby cried after swallowing Enfamil; crack appeared in Enfamil container); hence the amendment. But it would be absurd to allow a company served with a summons and complaint or other legal claim to obtain an indefinite extension of its duty of notice simply by hiding the claim from its Director of Risk Management. Especially when the claim is as large as PBM's claim, filed by a competitor who had obtained more than $46 million from Mead in settlement of two previous suits both quite similar to the one that Mead failed to notify its insurers of in timely fashion. The fact that the notice provision relating to a claim or suit was not amended to require notice to the Director of Risk Management can't be considered an oversight, though oversight or not Mead would be bound by the amendment's unequivocal language.

Remarkably, in its opening brief on behalf of its client Mead Johnson, the well-known law firm of Cadwalader, Wickersham & Taft argued that the amendment does apply to claims and suits as well as to occurrences, because the caption of the amendment is "Duties in the Event of Occurrence, Offense, Claim or Suit." That is a misrepresentation. The caption is "Duties in the Event of Occurrence, Offense, Claim or Suit, a. is hereby deleted and replaced with the following," the "following" being the passage relating to notice to the risk manager of occurrences, not claims. The new provision "a," like the old one that it replaced, begins: "You must see to it that we are notified as soon as practicable on [sic] any `occurrence' or an offense which may result in a claim." ("Offense" is not defined, but the policy contains a list of covered "offenses," such as copyright infringement—and, as we'll see when we come to the second suit by Mead Johnson, product disparagement.) Claim and suit are mentioned not in provision "a" but in provision "b," which contains no reference to the Director of Risk Management. The amendment changed only "a," which pertains only to occurrences.

Cadwalader's frivolous interpretation, though exposed in the insurance companies' brief, is repeated in Mead Johnson's reply brief and was defended by Cadwalader's lawyer for Mead at the oral argument. That a major law firm would engage in such shenanigans distresses us. The firm's argument regarding the amendment to the National Union insurance policy is censurable, and we hereby censure it.

The Lexington policy contains no reference to notice to a Director of Risk Management or equivalent official. But Mead argues that PBM's lawsuit could not be said to be "reasonably likely" to trigger Mead's excess coverage under the Lexington policy until the jury returned the $13.5 million verdict. Yet well before then Mead must have realized that a judgment in excess of $2 million, a judgment that would trigger its excess coverage under the Lexington policy, was "reasonably likely" in view of the outcome of PBM's previous suits.

Although Mead Johnson thus failed inexcusably to comply with the notice provisions in its liability insurance policies, such a failure allows an insurer to disclaim coverage only if the insurer is harmed ("prejudiced," in law-speak) by the late notice. Late notice does create a presumption of harm, thereby shifting to the insured the burden of producing "some evidence," Miller v. Dilts, 463 N.E.2d 257, 265 (Ind.1984); see also Tri-Etch, Inc. v. Cincinnati Ins. Co., 909 N.E.2d 997, 1004-06 (Ind.2009); Republic-Franklin Ins. Co. v. Silcox, 92 F.3d 602, 604-05 (7th Cir. 1996) (Indiana law), but probably does not shift the burden of persuasion. 13 Lee R. Russ & Thomas F. Segalla, Couch on Insurance § 193:41, pp. 193-62 to 193-65 (3d ed.1999); see also Jennings v. Horace Mann Mutual Ins. Co., 549 F.2d 1364, 1368 (10th Cir.1977); Alcazar v. Hayes, 982 S.W.2d 845, 856 (Tenn.1998).

National Union is unlikely to have incurred any harm from the late notice. Its policy limit was only $2 million, and we are hard pressed to understand how, had it conducted the defense of PBM's suit, it could have obtained either a jury verdict or a settlement of less than $2 million. Not only did the jury award PBM damages of $13.5 million; Mead Johnson used the same law firm, and the same lawyer in that firm, to defend itself that National Union had retained to defend Mead in PBM's previous lawsuits. How could National Union, using the same lawyer, expect to have obtained an outcome almost seven times as favorable to Mead as Mead obtained? What would it have told the lawyer to do differently? It doesn't say. Would it have found a better lawyer? It doesn't say.

It's true that had it defended Mead, National Union would have had to pay not only $2 million toward the judgment (although there is a dispute among the parties, unnecessary for us to resolve, over whether the $2 million would just have been a loan to Mead) but also the law firm's fee, and related expenses, for handling the defense. But National Union does not argue that it would have paid the law firm less than Mead Johnson paid it. And had it skimped on legal expenses the jury's verdict might have been higher and Mead might have challenged the adequacy of the defense and sought damages from National Union for breach of its fiduciary duty (noted earlier in this opinion) to its insured. See Lozier v. Auto Owners Ins. Co., 951 F.2d 251, 255 (9th Cir.1991).

We are tempted not only to reverse the judgment in favor of National Union (regarding the PBM suit—we take up the class action suit later), but to direct the entry of judgment for Mead. We are reluctant to do so, however, as there has been no factual development in the district court concerning the issue of harm. It's true that at the oral argument we pressed National Union's counsel on whether it could show harm from Mead's very late notice of PBM's suit and that she essentially conceded that she could not. But we hesitate to base a decision on a concession made in the heat of oral argument under a barrage by the judges.

Lexington's situation is different from National Union's. The limit in its excess policy was $25 million. Conceivably if placed in control of the defense it could have bargained to a settlement of less than $13.5 million or, failing that, have presented evidence or argument that would have convinced the jury to award PBM less. The problem is that the insurers' joint brief says almost nothing about Lexington, treating it rather as the tail to National Union's kite. (Maybe this is because the companies are siblings, both being subsidiaries of AIG, as we noted.) The brief implicitly assumes that Lexington, if in control of the defense, would (like National Union) have retained the same law firm that Mead Johnson did, and that the law firm would have employed the same litigation (including settlement negotiations) tactics.

So the insurers have thus far been unable to show what difference it would have made had they rather than Mead Johnson hired the (same) law firm to handle Mead's defense against PBM. But by the same token Mead Johnson has yet to present evidence, beyond the bare facts that the same law firm would have represented it had the insurers provided the defense and that $13.5 million is less than $41.5 million (the amount of one of the previous settlements by Mead with PBM), to rebut the presumption of harm from untimely notice.

There would be no need for an evidentiary hearing on the issue of the harm done to the insurers by Mead Johnson's untimely notice of PBM's suit had the district judge been correct in ruling that when untimely notice is given to insurer (in this case insurers) by an insured after the trial in the underlying suit, the presumption of harm becomes irrebuttable—in other words, that when notice is that late the insurer is off the hook. Period. (This assumes that there is no excuse for the late notice, such as a failure of mail delivery, as noted in such cases as McCarty v. Astrue, 528 F.3d 541, 544 (7th Cir. 2008); Prizevoits v. Indiana Bell Telephone Co., 76 F.3d 132, 133-34 (7th Cir. 1996), and Ramseur v. Beyer, 921 F.2d 504, 506-07 (3d Cir.1990), though none is an insurance case. There was no such excuse in this case.) The Indiana Supreme Court has never so ruled. It has always described the presumption as rebuttable. Delay could be forever, yet the insured be unharmed.

The judge was misled by two decisions of Indiana's intermediate appellate court that treat the presumption of harm from late notice as unrebuttable if notice isn't given until after the suit against the insured has been tried. Allstate Ins. Co. v. Kepchar, 592 N.E.2d 694, 699 (Ind.App. 1992); Milwaukee Guardian Ins., Inc. v. Reichhart, 479 N.E.2d 1340, 1343 (Ind. App.1985). They do so on the ground that the loss of the insurer's opportunity to make decisions on the conduct of the trial, a loss that is irrevocable once the trial takes place, deprives the insurer of a valuable right. But that deprivation is not a tangible injury—a loss for which damages can be awarded—nor, if the insurer could have done no better in managing the defense at trial than the insured did, even a cause of injury. The two decisions we just cited thus are inconsistent with Miller, and so we would not expect the Indiana Supreme Court to approve them. See also Erie Ins. Exchange v. Stephenson, 674 N.E.2d 607, 611-13 (Ind.App.1996); Mechanics Laundry & Supply, Inc. of Indiana Shareholders Liquidating Trust v. American Casualty Co. of Reading, PA, 1:04-CV-1122 DFH-TAB, 2007 WL 1021452, at *5-8 (S.D.Ind. Mar. 30, 2007). There is no indication that the Indiana Supreme Court will retreat from its position that the presumption of harm to an insurer from untimely notice is rebuttable. Maybe it should; indeed, maybe a flat rule that untimely notice, unless there is a good excuse for it, cancels coverage would be superior to existing law, given the inherent uncertainty involved in calculating the injury to an insurer of being deprived of control over the insured's defense to the tort suit that gave rise to the liability that he wants the insurer to reimburse him for. But that is an issue for Indiana, not for us. Indiana law, as stated in the Miller case, holds to the principle that if an insured inflicted no cost on his insurer by untimely notice, with the result that the insurer lost nothing by virtue of the untimeliness, then to allow the insurer to reject the insured's claim would confer a windfall on the insurer. In effect the insurer would be awarded damages equal to the insured's claim even though the insurer had not been injured at all.

To be consistent with Indiana law, the district judge should have said that the later the notice the harder it is for the insured to rebut the presumption that the insurer was harmed by being deprived of the opportunity to control the defense. It's because that's a rough row for the insured to hoe that a trial is necessary to determine whether the lateness of the notice in this case was indeed harmless, as it appears to have been on the present, limited record.

The second question presented by these appeals is whether National Union was entitled to decline coverage of Mead Johnson's coverage claims resulting from the consumer class action against it. Lexington is not a party to this suit; we haven't been told why. The suit was settled two years ago for approximately $15 million.

The issue is not notice to the insurer, which was timely, but whether the claim in the class action is within National Union's coverage of liability for advertising injury, defined in the policy to include "oral or written publication, in any manner, of material that ... disparages a person's or organization's goods, products or services." We have said that in contrast to a defamer, a "product disparager gets sales unfairly from a competitor by making the consuming public think that the competitor's product is of lower quality than the disparager's—implying... that the disparager's product or service is of higher quality than it is." Curtis-Universal, Inc. v. Sheboygan Emergency Medical Services, Inc., 43 F.3d 1119, 1124 (7th Cir.1994); see also Aetna Casualty & Surety Co. v. Centennial Ins. Co., 838 F.2d 346, 351 (9th Cir. 1988). National Union's policy requires "pay[ment to the insured of] those sums that the insured becomes legally obligated to pay as damages because of ... advertising injury," defined in the policy as including product disparagement.

The members of the class are consumers who bought Enfamil in preference to cheaper brands of infant formula on the basis of the same false representations by Mead Johnson that underlay PBM's suit. That is a claim of consumer fraud rather than of product disparagement. Consumers do not sell infant formula and so no product sold by any member of the class was disparaged. Rather, Mead Johnson's disparagement of PBM's product induced consumers to buy Enfamil, a more expensive product than they would have bought had it not been for that disparagement. In short, the class action involves no claim of product disparagement.

But Mead argues that National Union's policy covers any tortious injury that can be traced to product disparagement, rather than covering just claims of product disparagement. Its reason is that the policy covers damages for an injury "arising out of" disparaging material. But that is imprecise. The policy says that the damages must arise out of the "offense," in this case the offense of product disparagement. Must in other words arise from a "claim for" product disparagement, rather than just "having its origin in" product disparagement. The offense in this case is not product disparagement but consumer fraud, which the policy doesn't cover.

Mead Johnson's brief attenuates "arising out of" by equating it to "flowing from," "having its origin in," and, in short, having merely some "causal link," even if the link is indirect. Such a chain of equations can't be taken literally, for that would imply that the claims in the class "arise out of" the invention of infant formula. Usually the next step of attenuation of causality beyond proximate cause is "but for" cause, as in but for the evolution of man from ape PBM's infant formula would not have been invented and so could not have been disparaged. Legal liability rarely reaches back to the first, a very early, link of a causal chain.

The most common meaning of "cause" when the word appears in a judicial opinion is "proximate cause"—the meaning of which remains opaque after two centuries of incessant invocation. See, e.g., United States v. Laraneta, 700 F.3d 983, 990-91 (7th Cir.2012); CDX Liquidating Trust v. Venrock Associates, 640 F.3d 209, 214-15 (7th Cir.2011); BCS Services, Inc. v. Heartwood 88, LLC, 637 F.3d 750, 754-55 (7th Cir.2011). All that's clear is that it does not mean but-for cause and so does not sanctify the absurd hypotheticals in the preceding paragraph.

Here is a less fanciful example of where Mead's capacious conception of "arising out of" could lead. Suppose that a mother who has been feeding her baby a store-brand infant formula made by PBM reads Mead Johnson's ad which states that "mothers who buy store brand infant formula to save baby expenses are cutting back on nutrition compared to Enfamil," PBM Products, LLC v. Mead Johnson & Co., supra, 639 F.3d at 118, or, worse, sees Mead's visual-acuity ad, reproduced below, that tells mom that if fed Enfamil her baby will see an adorable rubber ducky with butterflies, while if fed a store brand, baby will be able to make out only a blurry yellow monster chased by bats. Mom, fearing that she has done irrevocable harm to her precious child, has a nervous breakdown precipitated by Mead's false, alarmist advertising. If she sues Mead Johnson for infliction of emotional distress, can Mead require National Union to defend and indemnify it on the ground that the mother's nervous breakdown arose from product disparagement? An affirmative answer—the answer implied by Mead Johnson's argument—would, by expanding coverage to remote consequences, make it very difficult for an insurer to estimate liability and thus fix a premium for injuries caused by product disparagement.

Mead cites four cases that it claims interpreted "arising out of" very broadly. One, E.R. Squibb & Sons, Inc. v. Lloyd's & Cos., 241 F.3d 154, 170-71 (2d Cir.2001) (per curiam), didn't involve causation. The other three interpreted "arising out of" in exclusions from coverage, such as an exclusion of "any claim which `arises wholly or in part out of' an illegal act." Bagley v. Monticello Ins. Co., 430 Mass. 454, 720 N.E.2d 813, 816 (1999); see also Continental Casualty Co. v. City of Richmond, 763 F.2d 1076, 1080-81 (9th Cir.1985); Underwriters at Lloyd's of London v. Cordova Airlines, Inc., 283 F.2d 659, 664-65 (9th Cir.1960). That's the opposite of interpreting "arising out of" broadly in order to expand coverage, which would make it difficult for an insurance company to fix a premium based on a reasonable estimate of potential liability—there would be no basis for rational estimation if "arising out of" has an indefinite extension. The Indiana courts agree. See Indiana Lumbermens Mutual Ins. Co. v. Statesman Ins. Co., 260 Ind. 32, 291 N.E.2d 897, 898-99 (1973); Westfield Ins. Co. v. Herbert, 110 F.3d 24, 26-27 (7th Cir.1997) (Indiana law).

This is not to say that the complaint in the underlying tort suit must use the words "product disparagement" for coverage to be triggered. A claim that fits the legal definition of product disparagement will trigger coverage even if the magic words are missing. Del Monte Fresh Produce N.A., Inc. v. Transportation Ins. Co., 500 F.3d 640, 643-44 (7th Cir.2007); Cincinnati Ins. Co. v. Eastern Atlantic Ins. Co., 260 F.3d 742, 745 (7th Cir.2001); Federal Ins. Co. v. Stroh Brewing Co., 127 F.3d 563, 566 (7th Cir.1997) (Indiana law). But a consequence is not a claim. Mead is trying to shoehorn one tort—product disparagement, which the insurance policy covers—into another— fraud, which isn't covered. That's a sleight-of-hand we rejected in the virtually identical case of BASF AG v. Great American Assurance Co., 522 F.3d 813, 820 (7th Cir.2008); cf. Rose Acre Farms, Inc. v. Columbia Casualty Co., 662 F.3d 765, 768 (7th Cir.2011). Mead Johnson tries to distinguish BASF on the ground that the tort claim giving rise to the insurance claim in that case was not fraud but instead a violation of antitrust law. Insurance companies generally refuse to cover antitrust liability because of the moral hazard problem (deliberate and often profitable wrongdoing, such as conspiring to fix prices, a core antitrust violation, would be encouraged if the conspirators were insured against damages for their misconduct) and the difficulty of estimating the likelihood and magnitude of the insured event. The same is true in this case, however. The consumer fraud of which Mead Johnson was accused is a form of intentional wrongdoing, and will be encouraged if the standard Commercial General Liability policy insures Mead against liability for such antics.

To summarize, the grant of summary judgment in favor of the insurers in the suit relating to the PBM litigation is reversed and that case remanded for further proceedings consistent with this opinion, while the judgment in favor of National Union in the suit arising from the class action against Mead Johnson is affirmed.

AFFIRMED IN PART, REVERSED IN PART, AND REMANDED.