You can have a Mexican woman run across the border, give birth on our land and that child is now a citizen by birth. Do you call that a natural born citizen? Could that child be President? I would love an answer on that! Good post. Transducer the troll doesn't get it, but our forbears already gave us an answer to your query in 1874: NO, that child could NOT constitutionally be President.
Hence Obama the Usurper.