My son was born overseas on a US Military Base. When we applied for his birth certificate and citizenship paperwork, we asked this very question. They explained to us that he has dual citizenship, could be anything he wanted to be, do anything he wanted to do as an American Citzien EXCEPT be POTUS. The Military Base did NOT qualify as American soil.
Tell your son to start raising money now for his Presidential race.
When you have a legal question, check what the law says and not the opinions of Gubbmint clerks chewing gum and shuffling papers.
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Article II, Section 1, Clause 5 of the Constitution: No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President
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You may have been told that but it is almost certainly incorrect.
US Citizenship and Immigration Services: Naturalization Eligibility
...the United States recognizes the U.S. citizenship of individuals according to two fundamental principles: jus soli, or right of birthplace, and jus sanguinis, or right of blood....
Certain individuals born outside of the United States are born citizens because of their parents, according to the principle of jus sanguinis (which holds that the country of citizenship of a child is the same as that of his / her parents). The U.S. Congress is responsible for enacting laws that determine how citizenship is conveyed by a U.S. citizen parent or parents according to the principle of jus sanguinis. These laws are contained in the Immigration and Nationality Act.
Information on who is a citizen or national at birth can be found in the following sections of the INA: § 301, § 302, § 303, § 304, § 305, § 306, § 307, § 308, and § 309.