Nothing is impossible, but remotely hacking a bank is pretty damn close. A number of years ago, a friend worked for a large multi-national bank. He once described to me some of the key components of the security system. While the details are hazy (such as I understood them at the time), I do remember that one of the key points was that one of the "very important" servers that handled transactions between outside entities (i.e. other banks) and internal systems was double-firewalled. That is, you couldn't initiate connections from the internet or the intranet. The server would only make connections to hosts of its own choosing, on its own schedule.

Modifying or updating anything on the server required physical access.

That server was located in a secure vault.