That turns out not to be the case. Those born outside the US, and citizens at birth via 8/1401, have been ruled to be “naturalized at birth”, in at least two Supreme Court cases. One as recently as the 1970s, IIRC.
Of course that only makes sense, since the power to define naturalization is the only power Congress has been delegated regarding citizenship. Since “naturalized” and “Natural born” do not intersect at all, such persons cannot be considered Natural Born Citizens.
Didn't say it did, I said the Supreme Court has ruled.... But while you are at it, the term Natural Born Citizen isn't in the code either.