I’m amazed to read this entire article and yet find that the applicable statute is quoted nowhere. Here is 8 USC 1401:

The following shall be nationals and citizens of the United States at birth: (c) a person born outside of the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions, prior to the birth of such person;

Unlike the original 1790 statute, this one no longer uses the term “natural-born.” Perhaps a lawyer can explain for me the difference between a “natural-born citizen” and a “citizen at birth.”