The Justice Department says JPMorgan (JPM). JPMorgan says an FDIC trust. The correct answer may not be the one you think.

Here are the facts: JPMorgan bought Washington Mutual, which had failed, out of receivership from the Federal Deposit Insurance Corp. in 2008. And despite the guffaws over JPMorgan’s contention that it should get all of WaMu’s good stuff, like billions in deposits, and not have to take all of the bad stuff, in this case billions in mortgage liabilities, that may actually be the case. Bloomberg’s Matt Levine calls this bonkers.

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But this was late 2008. Getting good banks to buy bad ones was not easy. JPMorgan did agree to swallow most of the costs of WaMu’s failure. But there were some costs the FDIC agreed to cover, and it set up a trust to do that. Much of the money to fund the trust came from the $1.9 billion JPMorgan paid for WaMu. For instance, the trust was suppose to pay for breaking leases on closed WaMu bank branches. Currently, there is $2.7 billion remaining in the trust, and about $13 billion in claims. The FDIC declined to comment on who put in the claims. But a former FDIC official said that most of the claims were for losses on WaMu bonds, which were also not covered by the JPMorgan deal.

Much of those bonds have since been bought by hedge funds that buy distressed debt — some people call them vultures — for pennies on the dollar. Earlier this year, some of those hedge funds, including New York-based Anchorage Capital, argued in court that the remaining money in the trust should be theirs. JPMorgan thinks the money should be used to pay investors who lost money on faulty mortgage bonds sold by WaMu, so that it doesn’t have to. A judge dismissed the hedge funds’ claim. But the court battle over who should get the money remaining in the FDIC’s WaMu trust continues.

And this is the fight that the Justice Department has unwittingly, perhaps, walked into with its settlement deal for JPMorgan. People close to the negotiations say JPMorgan has no plans to sue the FDIC for money in the agency’s general insurance fund. But the bank wants to preserve its ability to put any damages it has to pay on WaMu mortgage bonds back to the trust, which again was mostly funded by JPMorgan’s own money. Still, even this possibility is unacceptable to the Justice Department.

Generally, prosecutors and regulators want the companies they are trying to punish to pay penalties themselves, or else it’s really not that much of a penalty or deterrent from breaking the rules next time. What’s more, politically it won’t look all that good if the FDIC ends up paying a portion of JPMorgan’s fine. Talk of the JPMorgan settlement not being fair was ridiculed by The Daily Show. Already, Moveon.org has a petition against allowing JPMorgan to get a tax break on the settlement.

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But when you look at who loses if JPMorgan is allowed to tap the FDIC WaMu trust for a portion of the settlement, it’s not clear why the Justice Department cares. It’s not the FDIC or taxpayers. It’s the bunch of hedge funds, which if the Justice Department gets its way will be able to walk away with the entire $2.7 billion on their high-risk gamble on WaMu bonds. Is this really the good fight?

And from a public policy perspective, forcing JPMorgan to pay could do a lot of damage. A key part of resolving the last financial crisis was matching up failing banks with safe ones. Punishing JPMorgan for WaMu, even if it got all the good stuff, might make it harder to find willing buyers next time. Some people have brought up the flip side of that, which is that forcing bond investors to shoulder these costs will cause the cost of borrowing for banks to go up.

But that’s exactly what we want. One of the problems of too big to fail is that it’s too easy for the banks to borrow, allowing them to pile on the leverage and ratchet up their risk of failing. “Who should bear the loss of WaMu, is an important public policy question, with huge ramifications for the next crisis,” says Washington, D.C.-based bank consultant Bert Ely.

I would argue “hedge funds” is actually the best answer for all of us, even if “JPMorgan” would be a more satisfying one.