I've worked with folks from around the world (including Central and South Americans), some can be touchy about it. Had to tell them "sorry, I, as an American, don't define these terms. Blame Europeans, not me".
"US", "America", "Americans" all have specific denotations... per EMEA, and hell, even Canadians.
It's like nicknames - if you have one, you didn't choose it. It was earned or applied by someone else.