Section 1409 (C) only gives US Nationality child born out of wedlock outside the US to a mother who is a US National. Not citizenship. All US Citizens are US nationals, but not all US nationals are citizens. (American Samoans are the only group that this applies to, but it also applies to some individuals in special circumstances, such as the child of an unmarried US national mother born abroad.
I realize that, but by his own public admission concerning his father's nationality, Barry doesn't even meet the criteria for being a US national, much less that of a natural born citizen.
Most Americans could care less about the differentiation of US Citizens, US Nationals, naturalized citizens and natural born ones. Tossing the legitimacy of his parents' marriage confuses the issue further.
IMHO, the nationality Barry himself stated on his college admissions papers is MUCH more important, because he made that statement after he legally became an adult.