I'm losing track of how this works, of late. Canadian-born Ted Cruz was able to run for president, with at least one state ruling that he was eligible[1]. Of course there were the made-up controversies about Barack Obama, which I think can be dismissed. John McCain, meanwhile, seemed to get some kind of clearance from Congress to be able to run, as we was born in the Panama Canal zone[2].
1. https://en.wikipedia.org/wiki/Ted_Cruz#Citizenship 2. https://en.wikipedia.org/wiki/John_McCain#2008_presidential_...