Do they? I never do that. I didn't realize it was such commonplace.
However, I have purposely been "the naive, arrogant, ethnocentric American" when I was in the presence of some pompous, jack-ass foreigner who had the attitude that all Americans were a bunch of yahoo, f*ck yeah, buckaroos simply because I knew I was pissing the person off. I know that I'm not that way, and since NONE of the people, American or otherwise, that I associate with are that way, I have to believe that those Americans are the minority and some people outside of the U.S. just have a distorted opinion of ALL Americans based on, what appears to be, the most popular American stereotype.
Have you guys ever noticed that most Europeans smell like rotten ass because they don't bathe daily? There's a stereotype for you guys from this side of the pond.
I just had to add ... Most Americans don't say "eh" after a sentence. That's our neighbors that border us to the North.