Some time ago, I was asked in a job application to disclose whether I was at the time employed by a certain entity. Yes I was.
It was critical that it not be known publicly that I was working on a particular project there. I'm really not sure how true this would have been, but let's say that the recruiter could make a pretty obvious guess as to what project I was on, based on my experience.
I balked at that point of the application, but is that way overblown? Would it have been okay to give a dishonest "no" if they had asked a revealing clarifying question in an interview? Clearly, my bank can see where the money's coming from, and in the zero-probability situation that a teller asked about it, I'd obviously just have to deflect.