I cant imagine a bank not wanting your money 
Well I do remember that when I first started working as a contractor, I had to open a new business account to pay my first paycheque into (since the cheque was in the name of my new limited company.) And to my amazement the bank that held my personal account refused to allow me to open a business account to pay the cheque into (because I had an existing consolidation loan with them and they refused to allow me to open a new account until that was cleared.) So in the end I had to open a business account with a totally different bank just to be able to pay the cheque in, which annoyed me no end.
Although it's not really comparable with what Nat's describing, since if I'd already had a business account then no doubt they would've accepted the money. I guess banking in those days was a more personal affair, and therefore more subject to the whims of the people concerned, so maybe this kind of thing was par for the course.