How is it 'making things right' to allow the fund to be drained by people who weren't affected?
Who are "affected?"
Let's say you work for me as a critical employee in my business. A third party attacks you on the street and the resulting injuries send you to the hospital. I have to close my business because I am deprived of your skills. Should I be able to sue your attacker because my business was affected by his attack on you?
What about the pizza place from which I buy pizza for all employees every Friday? Do they have a claim against the attacker because their business has gone down?
What if you were not attacked, but were instead injured when a car's tire blew out sending the vehicle careening into you? Would I, or the pizza place, have a claim against the driver or owner of the car?
In these situations, both myself and the pizza place would be indisputably affected by your injuries.
In general, recover for tort law extends a limited way. The pizza place wouldn't have a claim in most cases because of this limited extension.
However, in the case of BP they agreed to pay out to parties whose stance was more attenuated than normally would be permitted in court. In return, BP's liability to those who signed on was limited.
BP's ad isn't about fraud. The ad was saying that the plain language of the settlement is being interpreted in a manner that is not consistent with the present philosophy of BP. The ad is saying "more people are getting money then we thought would" not "people are defrauding us."
To which I say: suck it, BP. You had your lawyers comb over the settlement. It was subject to numerous board meetings. In the end you made the determination that it was in your best interest to expand the class of parties who could initiate claims beyond what would normally be permitted in court in return for limited liability. I refuse to believe that such a decision was made without contemplating its broad consequences. If you failed in your ability to make an accurate determination as to what you would have to pay out then on your head be it.
If BP genuinely thinks it is getting taken advantage of then the proper means is to challenge the recipients of the funds using the systems laid out in the settlement or to challenge the settlement itself. Resorting instead to an absurd piece of demagoguery by buying ad space in the Times is simply demonstrative of a childish inability to confront their problems head on.