Yes, and they can't do that since the blockchain is public and can be verified by anyone with a node.
Lightning may be a different story but even there, the channels should be verifiable.
So if you go to a bank and don't check that they actually have your funds somewhere on the blockchain, that's on you.
For example, you can ask them to sign a message.
Also, you should use a 2of2 multisig. Else, they can just tell multiple people about the same funds.
Yes, and they can't do that since the blockchain is public and can be verified by anyone with a node.
Lightning may be a different story but even there, the channels should be verifiable.
So if you go to a bank and don't check that they actually have your funds somewhere on the blockchain, that's on you. For example, you can ask them to sign a message. Also, you should use a 2of2 multisig. Else, they can just tell multiple people about the same funds.