In the four years since the Deepwater Horizon oil rig exploded in the Gulf of Mexico, BP has gone from eating crow to crowing. In a recent op-ed, John Mingé, the chairman and president of BP America, celebrated the end of the company’s cleanup operation in the Gulf. “No company has done more to help a region recover after an industrial accident,” he claimed. Meanwhile, in court and in other media outlets, including 60 Minutes, BP is trying to get out of the terms of the mass settlement the company entered into back in 2012, when it was still humbled by the disastrous spill.

BP’s change of heart is, frankly, outrageous. And what’s at stake isn’t just the company’s obligation to pay an untold number of businesses as promised, but the integrity of other settlements like this one. If BP gets to wriggle out of the terms it agreed to, future plaintiffs negotiating the resolution of a group lawsuit (called a class action) will be less likely to trust such agreements. And that would be a shame, because settling big cases is in everyone’s interests: Defendants, their investors, and claimants all benefit from the certainty the settlement of a class action brings.

That settlement BP signed in 2012 requires the company to compensate those who suffered business losses after the spill, as long as they were located within a broad geographic area (stretching all the way to the Tennessee border). BP now claims that this allows recovery to all kinds of businesses that don’t seem at all connected to the spill. It shrewdly offers colorful examples—a five-figure award collected by George Morris, the owner of a high-end shoe store in Sarasota, and an award to an escort service.

But claims like these were always part of the deal. BP agreed to broad terms to gain predictable, easy-to-administer results. There was good reason for the company to choose that. It’s true that economic loss claims—as opposed to claims for personal injury—are much harder to prove than the typical personal injury case. Who knows whether a distant hotel, or even a retail store nearby, lost business because of the oil spill or for any of a zillion other reasons—sick employees, the bad economy, changing tastes in shoes. On the other hand, defendants worry that, given the ripple effects of a major disaster, too many people will be able to prove their losses were caused by the bad conduct.

Shortly after the spill, BP, under heavy pressure from the White House, agreed to establish a compensation fund. It was run by Kenneth Feinberg, whose track record as a fund guru is unparalleled. The complexity of dealing with economic loss claims meant that Feinberg proceeded on a case-by-case basis, shelling out an average of $26,000 each to about 240,000 people. It’s impossible to know whether any particular claimant would have done better by going to court, but $26,000 isn’t a lot of money, and many people and businesses recovered nothing. Plus the whole process lacked transparency.

So many claimants chose instead to opt out of the fund and proceed in the old-fashioned way: by suing BP. When they settled in 2012, the terms were these: Whether or not a business could prove that the spill caused a loss in revenue, it was entitled to recover if its financial pattern was in the shape of a V—revenue went way down after the spill and then rebounded strongly.

Of course, again, businesses fall and rise for all kinds of reasons. But until recently, BP had no problem with paying claims according to this formula. In late 2012, BP lawyer Mark Holstein even acknowledged that the settlement contemplated “false positives.” Now, though, BP Senior Vice President Geoff Morrell is saying: “No company would ever agree to a settlement that compensates people who were not harmed by their actions and we most certainly did not agree to such a settlement.”

That’s just wrong. In order to settle disputes, companies routinely agree to pay dubious claims. That’s why BP has gotten nowhere in court. In a decision in March, a federal appeals court held the company to the plain language of the settlement: As Judge Leslie Southwick wrote: “There is nothing fundamentally unreasonable about what BP accepted but now wishes it had not.”

What did BP get for agreeing to the terms it is bound by? Clear limits. Alongside the people who seem to be getting money for free are those who probably should be eligible to recover, but can’t. One plaintiff’s attorney said he’s had to turn away most of the folks that come to him seeking representation, because they can’t pass the V-test. For example, a marine construction business lost huge amounts of revenue right after the spill, when all the boats it would usually have worked on left the area to participate in the cleanup. But then the business didn’t bounce back quite enough to reach the top of the V.

That’s how it goes with settlements like this—you pay out for some cases where you shouldn’t, but you don’t pay out in other cases where you should. Investors go for it, because, all told, they see a better outcome than years of litigation, appeals, and uncertainty. As John Goldberg, a law professor at Harvard who has followed the BP case closely, reminded me, after Merck agreed to shell out almost $5 billion to settle claims that its painkiller, Vioxx, caused heart attacks and strokes, the company’s stock actually rose. That testifies to the value investors place on finality and certainty. Corporations everywhere should hope that BP loses its misguided bid to undermine both of those values.

Slate thanks John Goldberg for his expert help with this article.