Pedantic or Latin American, in my experience; it's not much fun to be forgotten, and I feel their frustration but can't think of a very good solution. "US-American" doesn't really roll off the tongue... Maybe the US could adopt the same ethnonymn as Usa, Japan? :P
Well they are South Americans then. In my experience (my Brazilian friends at least) they prefer being called Brazilian. Nobody except those with an axe to grind or more time than is good for them care that people from the United States of America are called Americans. I really wish people would just grow up and stop caring about stupid little things like that.
Or people for who English is not their first language. In Spanish at least, an "americano" is anyone from the Americas. People from the US are "estadounidenses".
It started with the Mexican-American war of 1846, so that is a viable theory (though the CIA was not yet involved). That's the war Mexicans still teach in every Mexican school with a big famous map showing that California and Texas are Mexican territory unjustly stolen by the USA.