Just looked it up. Goldater was born in the territory of Arizona in 1909 and Arizona was added in 1912 as a state.
He was born in a United States territory, and thus was a "natural born citizen". Read the wording of the relevant paragraph in Article II Section 1. I think it could be interpreted to mean someone born to an American citizen overseas could still become president. A child born to an American citizen is an American citizen by birth not naturalization.
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; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.