They're not insisting anything though right? They've only said it's funny and confusing. That you consider them to be insisting is interesting. I'm British so I've never been on the receiving end of any of that insistence, but from your response I assume it must happen frequently.
What I really want to contribute here though is that your "we" from "what we call ourselves" doesn't include me. Like a lot of people outside the US, English is my native language and calling Americans Americans has always given me pause for thought. So I put it back to you:
Is it even possible for us to be wrong about what we call you?