Yes, “America” could be the United States of America. But Chile is America, too.
Doubt that the Chileans would say that, certainly not in English. They know that they are on South America (a continent), so called to distinguish it from North America (another continent).
"America" (unqualified) is not the name of a continent. When it is used to refer to a particular polity, everybody knows what it means, even if that meaning is not "official".