So I think this comes from the fact that the country Americans have the most interaction with is Canada which has provinces instead of states, after that they might have some conception of how the UK works. Of course Mexico has states but most Americans don't really bother to learn much about Mexican political structure. Another possibility is that the American states have a lot of constitutional authority and I suspect (without doing research) that most countries don't give as much power as we do to their individual states.

Also a common reference for America used by non Americans is "the states"