I wouldn’t be so sure. I (a European) have occasionally used “American” in that sense when speaking English in a group of foreign students in Europe that included one from Latin America, and he somewhat pointedly substituted “from the States” etc. in his replies. He never went as far as correcting me, and I never explicitly asked if that phrasing annoyed him, but it seemed like it did.

Of course, there’s a substantial difference between annoying and offending, but it seems like there are, in fact, reasonable people who object to that usage.