I think McCain was the exception that disproves the rule, in terms of natural birth. The circumstances of his birth could not have been expected by the founders (lived infant years in panama as part of a military occupation force of territory extracted from that country after we separated it from colombia), then elsewhere) in the natural birth clause.
I DO believe it was meant to exclude people with claim to US citizenship who had been born and raised abroad (read - england, france, etc) from returning and having any ability to run for president. Needless to say, the Chester Arthur issue says a lot on what Obama’s claim to natural born citizenship is, no matter where he was born, unless another father is on his bc.