No. Here's the Minor citation:
At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners.
Under the SCOTUS definition, as with Vattel, "native" is the primary term. Therefore, under this (and Vattels') definition of native (i.e., native born), one must be born in the country to citizen parents. Natural-born is the same, so technically native-born = natural-born, but BOTH require citizen parents as defined by the Supreme Court.
I've seen "native born" being applied to describe the set of people born on the land, without any consideration whatsoever to the citizenship or allegiance of their parents, hence my confusion.