It may be irrelevant what anybody said, but it is not irrelevant what lots and lots of people said. For large chunks of the world, "Americans" meant "citizens or residents of the United States of America", long before Hollywood took its first reel of film.

> It's no different than if the most powerful European country were to call themselves Europeans alone.

Assuming always that it had established itself as the Federal Republic of Europe or some such before anybody else claimed the name.