Mitt Romney's father was born in Mexico. So how could he run for president?

This isn't meant as an expose or attack of any kind. It's just something I was thinking about during all the Romney biopics at the Republican Nation Convention (and CNN's Romney Revealed!) Mitt's father George Romney was a popular governor of Michigan and was briefly the front-runner for the Republican nomination for President when he ran in 1968. (He dropped out after a series of gaffes.) But George Romney was born in Chihuahua at a Mormon colony there. So how could he have qualified to be president if he was born in Mexico? 

When John McCain was running for president in 2008, congress quickly passed some sort of an exception allowing people born on U.S. military stations abroad to qualify for president. (McCain was born in Panama.) But that was in 2008, and a Mormon polygamous colony is hardly the same deal. Did anyone ever ask to see Romney's birth certificate? 

I'm just wondering because this seems to not make sense.

UPDATE: I just found this on Wikipedia: 

Questions were occasionally asked about Romney's eligibility to run for President due to his birth in Mexico, given the ambiguity in the United States Constitution over the phrase "natural-born citizen". His Mormon paternal grandfather and his three wives had fled to Mexico in 1886, but none of them ever relinquished U.S. citizenship. Romney's parents chose U.S. citizenship for their children, including George.The family fled Mexico and came to the United States in 1912 during the Mexican Revolution. By February 1967, some newspapers were questioning Romney's eligibility given his Mexican birth. In May 1967, the Democratic chair of the House Judiciary Committee, Emanuel Celler, said he had "serious doubts" about whether Romney was eligible, but had no plans to formally challenge the matter. Another member of Congress made a case against Romney the following month. In response, the New York Law Journal published an article by a senior attorney at Sullivan & Cromwell arguing that Romney was, in fact, eligible. The Congressional Research Service also came down on Romney's side, as did most other constitutional experts at the time. During the campaign, Romney was generally considered a viable and legal candidate for United States president. He departed the race before the matter could be more definitively resolved, although the preponderance of opinion since then has been that he was eligible.

That's pretty interesting that, 45 years ago, someone who was known to be born in Mexico - and four years ago, someone who was known to be born in Panama - was generally considered eligible to run for President. Or that the interpretation of "natural-born citizen" has changed over the years. Perhaps it's time to revisit how much sense that vague and xenophobic qualification makes in the 21st century, especially when it's only uses are to prevent qualified people from being president, and to fuel a racist conspiracy theory against a sitting president.