Bank systems are often not, in fact, ACID. Think of how many billions of transactions are processed in end-of-the-day batch runs, for example. Overdrafting is not only not impossible, it is a ludicrously profitable feature of the system.

How is this secure? Velocity limits, sophisticated anti-fraud systems, acceptable losses, and, as a bit of a by-the-way, the fact that people who make a habit of defrauding banks generally have a few weeks prior to being woken up by very serious men with guns.