The usage of the word as it is common in the USA is incorrect

Etymological prescriptivism is not really a tenable point in linguistics. You can argue that, for instance, in American English the Dutch word 'rekening' (bill) is abused as reckoning. And you can find literally thousands of examples like that.

I'm this case a non native speaker used the American English vernacular correctly. You argue that the word is used incorrectly in this vernacular, and it is very peculiar and steeped in the racial discourse of the country. However it's usage was correct in this case.

It all started with a dude looking at skulls, he saw one that was the most symmetrical, the best looking skull he ever saw. He decided it must belong to a white European, as they are the best people (/s). He finds out that the skull was that of a person from the Caucus mountains.

Caucasian has been used to describe the ‘superior’ white Europeans since. So, OP is using the word correctly really. They say African, Asian, Latino because those are other races… with unpleasant skulls.

This is a gross oversimplification, but one of the modern excuses for racism and race superiority. Also, why ‘Caucasian’ is used to say white European.

Two reasons spring to mind:

1. Certain parts of the US equate "Europe" with being effete or weak, and also socialist. Not saying it's right but it is a thing they believe.
2. Some people prefer more granularity, so they'll describe themselves as "Irish-American" or "Italian-American". This stems from the waves of immigration the country experienced, wherein each new wave was often on the receiving end of racism.