That is correct- there are all sorts of human and procedural buffers built into bank operations. Correctness of the system- and there is never just one system,

That is correct- there are all sorts of human and procedural buffers built into bank operations. Correctness of the system- and there is never just one system, there are at minimum dozens, even in the smallest bank- is not a hard requirement. In fact you would immediately seek another job if you came from formal methods practice and then saw production code at just about any of the different animals called banks.