If the parent left the other country before the child was born and naturalized before the child reached majority, then I'm saying there would be less reason to challenge the child's claim of natural born citizenship. The child would have grown up in a home in this country with parents whose allegiance was to this country. That's pretty much what natural born citizenship is all about.
That would seem reasonable in this day and age - but absent a Constituional Amendment, we are talking about what the Founding Fathers understood at the time they wrote the Constitution. The father would have had to have been naturalized prior to the child's birth.
On what basis?