I am an estates & trusts paralegal. In my experience, each bank is different, and most of them make up their own rules when they don't know what to do. Also, the Patriot Act has put paid to common sense anyway. I have never heard of a bank doing that though, wow.
Honestly, if it were me, I'd probably take all of that documentation and try another bank that actually wants your business and isn't suspicious of your paperwork, which all sounds perfectly in order to me.