I don't think that's correct, per this from above:
As originally enacted, section 301(a)(7) stated: Section 301. (a) The following shall be nationals and citizens of the United States at birth: (7) 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 ten years, at least five of which were after attaining the age of fourteen years:"
I stand corrected. The unwed rule only applies if birth in the US.