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I believe I read somewhere that if coins are sent to bittrex with the wrong memo they are under no legal obligation to return them, but instead are treated as a donation. Now, I don't think for one second Bittrex will go that route in this particular situation, but it looks like legally, they could.

Bittrex technically has possession of the coins, but due to AML they can't declare them as donation as there is maximum number of transferable coins that is exempt from AML.

Basically any large amount of currency is by default assumed to be criminal in origin, unless proven otherwise... As the account where they were sent was accessed by someone other than intended user of the account, they can't possibly prove the legitimate origin of the coins.