According to the Foreign Affairs manual published by the U.S. Department of State, statutory citizenship (i.e. granted by U.S. statute at birth) may or may not be equivalent to natural-born citizenship under the U.S. Constitution.
7 FAM 1131.6-2 Eligibility for Presidency
(TL:CON-68; 04-01-1998)a. It has never been determined definitively by a court whether a person who acquired U.S. citizenship by birth abroad to U.S. citizens is a natural born citizen within the meaning of Article II of the Constitution and, therefore, eligible for the Presidency.
(...)
d. (snip) In any event, the fact that someone is a natural born citizen pursuant to a statute does not necessarily imply that he or she is such a citizen for Constitutional purposes.
From here, the discussion typically progresses to Ted Cruz. So before you ask, yes, I believe Cruz is eligible. However, the courts have not ruled on it. See here for my logic on Cruz: http://www.freerepublic.com/focus/bloggers/3289769/posts?page=102#102