The first dictionary I looked up used the USofA as the first definition.
Webster has #3 as a "citizen of the United States". Nowhere in that definition does it ever get specific about a citizen of 'Mexico', or a citizen of 'Canada', as it does for US citizens, meaning American IS a term describing citizens of the United States; And NOT used for describing Mexicans unless only in part as a larger group of inhabitants of the whole North and South American continents.
Furthermore, I seriously doubt this person was lumping in Chileans, Canadians, Mexican, and Cubans etc when he referred to 'americans'.
Please use some common sense.
I am using common sense. My original post was just a single sentence, since that was all there should have been needed to show that there are alternative, but valid, uses of the term. That really should have been enough.
But common sense includes the view that US of A puts one weight on the meaning of the word. That weight is not the same in all other parts of the world. So common sense is to not use a sledgehammer in a international web forum.
Mighty off-topic but the New York Times Manual of Style and Usage (1999) America says that the "terms America, American(s) and Americas refer not only to the United States, but to all of North America and South America. They may be used in any of their senses, including references to just the United States, if the context is clear. The countries of the Western Hemisphere are collectively the Americas ". So even within USA, the term is acknowledged to be usable in multiple situations.
In the end, the definition of what is "common sense" or what is "clear context" does vary. That makes it common sense to not jump on someone using "american" about a canadian even if a canadian would normally not like to be called american because of the great risk of confusion.