You are a brave soul! When dealing with my local tax collector I want as much of a paper trail as I can get. My township uses a part-time tax collector who's organizational skills are a little wanting.
I think you are wise.
I too live in a small town, and my guess is that any mistake on this lies with with town. It could be that I screwed up something, but I don't think so. BofA does not seem to make mistakes.
The city office is just down the road from me. It is very easy to go down there, pay the bill, and get a stamped receipt. That is what I will do in the future.
Also, if the city screws up on something like an electronic payment, they will still charge you a 10% penalty. They can't do that if you have a receipt.