Wong Kim Ark, 169 U. S. 649 (1898)
Montana v. Kennedy, 366 U.S. 308 (1961)
Rogers v. Bellei, 401 U.S. 815 (1971)
Fiallo v. Bell, 430 U.S. 787 (1977)
Miller v. Albright, 523 U.S. 420 (1998)
Tuan Anh Nguyen v. INS, 533 U.S. 53 (2001)
Other than Wong Kim Ark (cited because it shows how the "two types of citizenship" argument is derived, and how it operates), the fact that those cases even exist, depends on the subject having naturalized citizenship (or arguing that they are entitled to naturalized citizenship).
None of those cases would exist if the subject was NBC. A different set of cases illuminates how one can lose US citizenship, and a first premise is that US "natural" citizenship can only be lost by voluntary action. The persons in the cases above did not volunteer to "lose" citizenship (Bellei lost his).
There are hundreds of cases in the Immigration Court books.
Concluded
From Rogers v. Bellei
"But it [the first sentence of the Fourteenth Amendment] has not touched the acquisition of citizenship by being born abroad of American parents; and has left that subject to be regulated, as it had always been, by Congress, in the exercise of the power conferred by the Constitution to establish an uniform rule of naturalization."
Ive see all those cases and none of those get to the issue.
It has NEVER been adjudicated.
Scalia dead. On to bigger things