"I know a girl, born to two US citizens while on vacation in Canada, who was not considered a US citizen."
Read USC 8 Section 1401 paragraphs (a) and (c).
http://www.law.cornell.edu/uscode/8/1401.html/a>
§ 1401. Nationals and citizens of United States at birth
The following shall be nationals and citizens of the United States at birth:
(a) a person born in the United States, and subject to the jurisdiction thereof;
(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;
Paragraph (c) appears to be applicable to this girl you know. We know by law she is a citizen at birth by this very paragraph (c). There is no denying this IMO.
Now read paragraph (a) and notice that it covers over 300 million people in the United States, including at least 40 previous presidents, you, me and most members of Free Republic. Since we are all citizens at birth including at least 40 Presidents of the United States, a citizen at birth MUST also be a natural born citizen.