I checked to be sure about US citizenship rules for children of US parents born abrad. The parents would have to go to the US embassy and fill out some paperwork and then the child becomes a US citizen. Tim Tebow was born in the Philippines. His parents were missionaries at the time.
I don't have any problems with that, it seems reasonable. But such a child should not then be considered "natural born".
Anyone born in another country is bound to have some feelings for that country (including some feelings of loyalty). And the longer that child was residing in that country, the stronger the feelings would be. The Founders wanted to avoid all that.
Yes, labeling such a child as not "natural born" might be unfair, and it would exclude many good people, I suppose. But IMHO it's not worth the risk.