See post 238 for the law on this. You are wrong, wrong as two left shoes.
Post 238 did not include all of the relevant Statute, such as:
The following shall be nationals and citizens of the United States at birth:
(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;
(g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years
http://www.law.cornell.edu/uscode/html/uscode08/usc_sec_08_00001401——000-.html
(g) would cover a situation where a child was born abroad to one citizen and one non-citizen.