I'm speaking as someone who has done a bit of research into this topic.

I'm not aware of a single example of an English-speaking country that teaches that there's a continent named "America." It's taught as two continents: North America and South America. "America" is just short for the "United States of America," and in English it's entirely unambiguous.

Even the phrase Americentrism undermines your point. This is like reading about a Dacian complaining about the Romans using the term Mare Nostrum. Nobody really pays any mind to the client states of an empire.