My bank did this. They had actually made a mistake on their end; one of their reps put a hold on my account (presumably a suspicious transaction), but didn't put it in right so it registered as being my request.

I called up, asking why there was a hold, they said I put it there, I said I didn't. There was a long pause, followed by "for security reasons, we won't be able to help you with anything related to your accounts until you come into a branch and present photo ID".

It was a bit inconvenient, but I have to say I was pretty impressed.