[ROCKLOBSTER]

If that's the case, then anyone in North America, Central America, or South America could be called an American.

Correct. (See: "names of continents")

Anyone from Europe is a European, people of Asia are Asians, Africa etc..."nationality" notwithstanding"

[HoneysuckleTN]

“American” has come to have a specific meaning, though.

We’ll have to agree to disagree. :)