I understand both sides, as I hate banks. I sued my last job which was a major bank. I tried to sue chase for discrimination but no one would take the case, and I tried to sue Wells Fargo for an incident involving my balaclava mask, but no one would take the case. I fukking hate banks.
That said, I have had more than enough experience with situations like dudes. And dude may not have broken the law, but he did have behavior that would possibly cause concern inside a bank.
I believe he was trying to be unnecessarily over discreet (which is his right) but that he put the teller on alert. The teller may or may not have been following protocol, but part of protocol may be them getting to may judgement calls. She probably legit felt something was off and was just wrong.