The following script is from "Over A Barrel" which aired on May 4, 2014, and was rebroadcast on Sept. 7, 2014. Scott Pelley is the correspondent. Robert Anderson, producer.

BP, the company responsible for the Deepwater Horizon disaster in 2010, is suddenly facing billions of dollars in higher fines. A federal judge ruled last Thursday that BP was "grossly negligent" in the biggest accidental oil spill the world has ever seen. And that the ruling means that fines could be quadrupled. Long before this ruling, BP had already paid billions in fines, and in compensation, to businesses hurt by the spill. But, as we first reported in May, BP is now crying foul, claiming it's the victim of Gulf Coast swindlers who have the oil giant over a barrel. BP says it's being forced to pay hundreds of millions of dollars in compensation to people who never saw oil anywhere but on TV.

The explosion was a catastrophe. Eleven crew members were killed. The gusher flowed 87 days. BP put up billions to pay compensation and hired attorney Ken Feinberg to sort out who was hurt by the spill and who was not.

Ken Feinberg: One fellow down in Alabama said to me, when I asked him for proof, he said, "Mr. Feinberg we do things with a handshake down here." I said, "That's fine, but a handshake won't get you compensation.

Scott Pelley: Why is it so important to hold everyone to that standard of proof?

Ken Feinberg: Because there'll be another catastrophe. And a catastrophe after that. What happens the next time, in terms of a company's willingness to do something similar?

Feinberg has long experience. He ran the compensation program for victims of 9/11. In the BP disaster, he told us there were often two kinds of applicants, the deserving and the devious.

Scott Pelley: What was the most outrageous claim you got?

Ken Feinberg: I think there was a fellow in Oslo, Norway, if I remember correctly who slipped on the ice while he was filing a claim and sought damages for a broken leg.

Scott Pelley: People saw money and they tried to get it.

Ken Feinberg: Human nature. Goes with the territory. I think that if you had any type of compensation program anywhere, you get a fair number of people who try and game the system to try and recover compensation.

Feinberg says, out of more than a million claims, he found only a third were justified. His critics said too many claims were being denied. So to avoid decades of court battles and uncertainty, BP agreed to a more lenient compensation program. But now BP Senior Vice President Geoff Morell says the oil giant is getting soaked by businesses with losses that are not linked to the spill.

Geoff Morell: We're talking about a wireless phone company store that burned to the ground and shut down before the spill. An RV park owner that was foreclosed upon before the spill. And I love this one. A Pontiac dealer who could no longer sell Pontiacs because GM had discontinued the line before the spill.

"Human nature. Goes with the territory. I think that if you had any type of compensation program anywhere, you get a fair number of people who try and game the system to try and recover compensation."

Scott Pelley: Those are all real examples and they are people who actually got a check?

Geoff Morell: Those are all real examples and are, frankly not exceptions but rather emblematic of a far larger problem. There are more than a thousand claims just like them that had glaring red flags associated with them that should have been picked out by the claims administrator and instead were ultimately awarded more than $500 million.

That's how BP adds it up, but the new claims administrator, Pat Juneau, says BP is getting what it asked for. Juneau's Deepwater Horizon claims center replaced Ken Feinberg. Same job, new rules.

Scott Pelley: BP makes it sound like you're throwing millions of dollars away to people who have no stake in the oil spill whatsoever.

Pat Juneau: I have an obligation as a court-appointed official by the federal court to implement what these two parties wrote.

The "parties" are BP and, on the other side, lawyers representing victims. They negotiated a settlement with a fairly simple formula. BP agreed to pay businesses whose income dropped after the spill, and then rebounded one year later. Trouble was some attorneys soliciting clients, took that to mean any business with a loss of any kind.

[Brooks/LeBoeuf: Your losses don't have to be directly traceable to the oil spill.]

[W.F. Casey: "Do I have to prove the oil spill directly harmed my business?" The answer is no.]

[Gusty Yearout/Lloyd Gathings: A business does not have to prove that their loss was directly caused by that event.]

Geoff Morell: There was a proliferation of these kinds of ads. And there was almost a pied piper like recruitment of claimants and compounding that problem was the fact that the claims administrator the facility began to pay these claims.

One attorney's flyer says, "The craziest thing about the settlement is that you can be compensated for losses that are unrelated to the spill." BP's attorney Ted Olson has a word for that.

Ted Olson: I think that's fraud. We want to compensate legitimate claimants. But this here's an incentive to encourage people to commit fraud and that that is wrong.

So BP launched its own ad campaign which pointed to $60,000 that went to colorectal surgeons 300 miles from the coast and 173,000 paid to an escort service in Florida. BP also claims $8 million was approved for companies that clean up after hurricanes. Their income was down after the spill, because there were no hurricanes that made landfall that year.

Pat Juneau, the claims administrator, told us he questioned the eligibility formula at the start, because it didn't require proof of a link to the spill. He asked BP about that. And BP replied in the court record, that if the numbers fit the formula "all losses...are presumed to be attributable to the oil spill" (even if) "the decline was...wholly unrelated to the oil spill." With that, Juneau decided that if a business lost money he was not allowed to ask why.

Jim Roy: It's a black and white formula, a deal is a deal, Scott.

Jim roy is a lawyer for the victims. He helped negotiate the eligibility formula with BP.

Jim Roy: Well, I think BP has buyer's remorse. BP told the court that it believed that this was gonna be a $7.8 billion dollar settlement. But I think it's gonna be considerably more than the amount of money that BP said it was gonna cost.

We called dozens of the applicants that BP says, took unfair advantage of the deal -- but all of them declined to be interviewed.

Scott Pelley: Do you think that might be because they're feeling sort of sheepish about receiving that check?

Jim Roy: No, I think there are two things going on. I think, one, most of these businesses understand that they want their lives to stay private. And number two, the last thing you want is to go on "60 Minutes" with Scott Pelley to broadcast anything about them personally.

But there could be another reason, on the claim form that applicants sign under penalty of perjury it says that they: "assert economic loss due to the spill." BP lawyer Ted Olson says it shouldn't matter that the formula to calculate the loss doesn't consider the cause.

Ted Olson: You had to have been hurt by the oil spill.

Scott Pelley: BP's accounting expert, Holly Sharp, testified in 2012 that once a business meets the formula, all losses are, quote "presumed to be caused by the spill with no analysis required to determine whether the declines might have been due at least in part, to other causes." I mean it just seems that that's what BP agreed to. You made your bed, and now you're lying in it.

Ted Olson: The part that you just quoted for me started off with, "Once you meet the formula." The formula is that first of all you have to establish that you were injured as a result of this. Otherwise anyone can walk in and say, "I had a bad year. Pay me money."

Scott Pelley: And that's exactly what's happening?

Ted Olson: That's exactly what's happening.

Scott Pelley: The front page of the settlement claim form says, quote, "The claim is for those that assert economic loss due to the spill." What does due to the spill mean to you?

Jim Roy: Caused. But if they qualify whatever that calculation is, they should be paid. You may, in hindsight judge, "That just doesn't seem right." I may judge in hindsight, although I don't that that just doesn't seem right. But that's the deal BP asked for. That's the deal BP got. And the deal BP got was for the entire states of Mississippi, Louisiana and Alabama.

Claims administrator Pat Juneau is rejecting about 40 percent of claims -- when companies can't prove an economic loss -- of some kind. But he has approved more than $3 billion in claims so far

Scott Pelley: So, in a nutshell, if they've got the right numbers they get a check?

Pat Juneau: I'm obliged to pay--honor and pay those claims.

Scott Pelley: BP essentially is saying that you're facilitating fraud.

Pat Juneau: I have never in my life--I'm 76 years old. I've been to a lot of rodeos in my life. I don't facilitate fraud. Fraud offends me.

Scott Pelley: But doesn't this do violence to common sense when you're paying claims to people who have no loss associated with the spill? How could that possibly be the intent of the agreement?

Pat Juneau: You do understand that I wasn't there when these parties agreed to this agreement. And that's what they agreed to.

Geoff Morell: But 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.

Jim Roy: BP doesn't like the deal it cut now. I'm sorry about that. I can't help that. But I was in the room when this section of the deal was negotiated. Others on our team were there too. That's what we saw and heard. No doubt about it.

The battle, of course, is in the federal courts. BP has won a few on the size of some of the checks. But it's lost every attempt to reinterpret the formula that decides who is eligible.

Scott Pelley: Here in New Orleans, one federal judge said that BP was essentially trying to rewrite the deal. A federal appeals judge said that there was nothing fundamentally unreasonable about the deal that BP agreed to but now wishes it had not. BP is now asking the appeals court for one more hearing.

"BP doesn't like the deal it cut now. I'm sorry about that. I can't help that. But I was in the room when this section of the deal was negotiated. Others on our team were there too. That's what we saw and heard. No doubt about it."

Scott Pelley: Is this a matter of BP's attorneys just having been hoodwinked? You accepted a deal without fully realizing what it meant and now you're stuck with it?

Ted Olson: No one could have anticipated that the system would go completely off the tracks, but that's why you have appellate courts. And that's why we have the Supreme Court. BP will take this as far as it is necessary to go to make sure that this settlement agreement is construed properly.

Scott Pelley: Did you guys take BP to the cleaners on this?

Jim Roy: No sir. BP got a good settlement. And BP was represented by very, very good lawyers who were worthy adversaries who fought tooth and nail for their client. And it was a hard-fought settlement. Their own lawyer said it was a very generous settlement.

Scott Pelley: That's not what they're saying now. There're saying it's a little too generous.

Jim Roy: It is what it is.

Now BP complains it feels like it's the visiting team fighting a home field advantage along a Gulf Coast that remembers vividly scenes like this.

Pat Juneau: If the inference is that we're giving preferential treatment and putting the screws to somebody here, myself or this court--that's grossly untrue. It's offensive, certainly offensive to me. And it shouldn't be said and it has no place in this litigation.

Shortly after our story first aired, the federal appeals court denied BP's request for another hearing on who is eligible for an award. And just this past week, BP asked another court to consider removing Pat Juneau as the claims administrator.