Sure, at some level the technology will come in to play but nobody will 'start a high tech bank'. For instance, ING direct (one of the efforts of the banking industry to leverage the use of technology) was jump started from the legacy ING systems and as far as I know still ties in to them for all of their back-end stuff.
When I was the 'systems administrator' for the corporate division of a bank (in 1986 or so) we had daily rounds of getting the signatures of the various people responsible that the totals for the night batch runs were correct. That's the sort of responsibility you're talking about, I can't imagine that an MD5 or some digital signature would be sufficient today, it's all about procedures and accountability, emphatically not about technology.
I got one of the first PCs the bank bought on account of our project manager being very forward thinking but nobody ever thought of it as more than a curiosity and something that might be a handy replacement for the terminals.
That attitude has changed a bit but not by much and that's 25 years.