Yes indeed. It's hard to come up with something that has the same international recognition. We are a country without a proper name, unlike Mexico, and Canada, both of which its populations can be called "(North) Americans" as well.
Except you would call them NORTH Americans, just as you would call South Americans--SOUTH AMERICANS.
Only one group of people in this world is called Americans and when you say "American" it is instantly associated with the USA. In fact, US is just a title for a Union of states, America is our name and we're the only country with America in our name.
Thus, we are the only Americans. I remember that nitwittery about other "americans" in college when learning Spanish. Nooooooo, there is only one American.