A pregnant illegal wades across the Rio Grande into the U.S. from Mexico where she has a baby. She eventually gets caught and she and her child are shipped back to Mexico, even though under current U.S. law, the child is a U.S. citizen.
A U.S. citizen soldier and his pregnant U.S. citizen wife are stationed in Germany where she has their baby.
Which offspring can be elected president or vice-president in the U.S.? The answer hinges on what your interpretation of 'natural born' means.