That's the advantage of letting your money to be saved in the bank. You are covered by the law when something happened unexpectedly to their bank, just like insurance and everything as long as that collapse will happen within the banks premises or the cause is the banks negligence. That's why I still trust them because of that.
Yeah you should not trust banks that doesn't recognize bitcoin transaction because it may scam you in the future, and make sure that bank has a a protection of your account. If the bank you are going to transact with does not meet that criteria don't do transaction with them, i myself trusted one bank in my country which i cash out my bitcoin wallet and it really done well in any transaction i had with them and still right now i am fully trusting them because of their safe banking transactions as well.