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Of course that was the common usage; it still is the normal and traditional English language usage of the word native; not to be confused with modern political correctness-ese usage:
noun
1. a person born in a specified place or associated with a place by birth, whether subsequently resident there or not.
"a native of Montreal"
adjective
1. associated with the country, region, or circumstances of a person's birth.
"he's a native New Yorker"
Distinguish between a native American, being one born in America, and a Native American or Amerindian, a member of one of the continent's indigenous peoples, through the use of capitialization.