Technically it's true that the depositor gives up "ownership" of his funds upon making a deposit, but in the US this is practically a moot point for most people

Technically it's true that the depositor gives up "ownership" of his funds upon making a deposit, but in the US this is practically a moot point for most people because of FDIC protections. Depending on the state (for example, "right of setoff" in NY) there may be some unusual corner cases, but in general crypto exchanges have far more power over your crypto deposits than traditional banks do over your cash deposits.