If you receive your doctorate in the US, then you can say “I became a doctor in the US.” Saying “Dr. funtush was born in the US” would be incorrect and laughable. Can Dr. funtush, not funtush, run for president of the US? No, because Dr. funtush was born in Nepal.

Where Buddha received enlightenment/education/epiphany does not change where he was born. Siddhartha Gautam was born in Nepal. Buddha was born in Nepal.