There is a huge difference between the skills necessary to safely hold your money and setting up HTTPS. I bet you that there are a lot of fraudulent banks that are very good with https, but aren't to be trusted.
In order to safely run an internetbank, there are a thousand of small things that all must be done right. If they can't even set up (and test, and verify, and maintain) https, what makes you think that they can handle 100% of the much more complicated computing security issues without missing something?
Except you example is false. I see no reason a quadriplegic couldn't serve as an ambassador.