That is what the word "native" means NOW. In the past, it didn't have the same meaning. Justice Waite (Minor v Happersett) explains what "native" meant in 1875.
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.
What evidence is there for a distinction drawn that you are drawing here? Absolutely none.
There is plenty of evidence for a distinction being drawn. Claiming there is none is either ignorant or dishonest.
Great argument - except Waite distinguishes between those born in America, and those who were not born in America.