14 Stat. 27; Fourteenth Amendment, § 1; United States v. Wong Kim Ark, 169 U. S. 649.
In a comprehensive review of the principles and authorities governing the decision in that case -- that a child born here of alien parentage becomes a citizen of the United States ...
Moore, Int.Law Dig., Vol. III, p. 543.
Secretary William M. Evarts, in 1879, in an instruction to our Minister to Germany with respect to the status of the brothers Boisseliers who were born in the United States of German parentage said:
"Their rights rest on the organic law of the United States. . . . Their father, it is true, took them to Schleswig when they were quite young, the one four and the other two years old. They lived there many years, but during all those years they were minors, and during their minority they returned to the United States, and now, when both have attained their majority, they declare for their native allegiance and submit themselves to the jurisdiction of the country where they were born and of which they are native citizens. Under these circumstances, this Government cannot recognize any claim to their allegiance or their liability to military service, put forth on the part of Germany, whatever may be the municipal law of Germany under which such claim may be asserted by that Government."
Foreign Relations, 1906, p. 657.
"Assuming that Alexander Bohn [the father] never became a citizen of the United States, Jacob Bohn [the son] was born of German parents in the United States. According to the Constitution and laws of the United States as interpreted by the courts, a child born to alien parents in the United States is an American citizen, although such child may also be a citizen of the country of his parents according to the law of that country."
Content and references here. And, of course, excepting those persons not 'subject to the jurisdiction' of the US due to the specific circumstances previously cited.
This assumes that no legal differentiation in US Law or the COTUS between 'native citizen', 'natural born citizen' and 'having citizenship at birth' can be found (as is thus far the case).
If you say, Birth on US soil = Natural born citizen, then two terrorists could come here give birth to a child and that child could grow up to be President. That is wrong.
The child would be a citizen, but not a “natural born” citizen because the parents were not citizens at the time of his birth.
Now if two persons come here and become citizens, then give birth to a child, then that child can grow up to be President because the child would be a “natural born” citizen.