No, it's your link that's Bullsh!t. English Common law and Supreme Court case law are very clear that a person born in the US to non-citizen parents is a natural born citizen so long as he is subject to US jurisdiction when he is born.
It's all laid out here:
http://www.obamaconspiracy.org/2008/12/natural-born-citizen/
It is an established maxim that birth is a criterion of allegiance. Birth however derives its force sometimes from place and sometimes from parentage, but in general place is the most certain criterion; it is what applies in the United States; it will therefore be unnecessary to investigate any other.
James Madison, May 22, 1789, House of Representatives