From an earlier edition, there’s a useful footnote referencing a book by Thach and another by Farrand that evidently provide further detail on the source of the NBC clause:
http://books.google.com.ph/books?id=p1o_AAAAIAAJ&pg=PA325&img=1&pgis=1&dq=natural-born&sig=ACfU3U3ty8VF5MKgQlUD8IOpUDO3T6rcOQ&edge=1
Thus, it’s easily possible Corwin relied on these authorities rather than Vattel directly.
Here’s a link to a nice review of Thach, apparently considered a highly authoritative source. Unfortunately, I can’t find it on Google Books. http://www.libertyfund.org/details.aspx?id=2021&catalog=090210
Thus, its easily possible Corwin relied on these authorities rather than Vattel directly."
The creation of the presidency, 1775-1789; a study in constitutional history by Charles Coleman Thach
http://www.archive.org/stream/creationofpresid00thac#page/n311/mode/2up/search/natural
Basically states that the requirement for a "Natural Born Citizen" most likely came from Jay's suggestion to Washington.