it was Bill Buckley himself who pointed out that liberals usually fail to make critical distinctions. Well, this is an example from his own magazine.
The critical distinction here is between the child of legal immigrants (who went home after their visa expired) and the children of illegal immigrants, those whose very presence here is illegal. It's one thing to argue that the birth of a child to a to an alien LEGALLY present in our country confers citizenship; it's entirely another to argue that this same principle applies to one who is here ILLEGALLY!
Except at the time the 14th was written there was no such thing as an illegal immigrant. After the fact we can try to guess how the amendment might have been worded differently, but as it stands the language doesn't draw any distinction.