That would be a non-standard account with a non-standard way of withdrawing money. EFT and ACH withdrawals are fully protected.
Money wires are different, all the action is sender side. Even for me, Fidelity accountholder, a SWIFT money wire takes days to set up and I have to confirm it multiple times. I get the impression the bank hates doing them and will throw as many roadblocks as possible unless you are absolutely committed to it.