By federal law -- I think it was cited specifically on this thread, but I'm not entirely sure.
In any case this federal law (particularly sec 1401) has a subsection saying:
The following shall be nationals and citizens of the United States at birth: […]As this is a federal law, and congress's is only power regarding citizenship is that of naturalization anyone claiming citizenship via that law is claiming to be naturalized.
(d) a person born outside of the United States and its outlying possessions of parents one of whom is a citizen of the United States who has been physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the birth of such person, and the other of whom is a national, but not a citizen of the United States;
Excerpt.
Similarly, in its first naturalization statute, Congress declared that
“the children of citizens of the United States, that may be born beyond
the sea, or out of the limits of the United States, shall be considered
as natural born citizens