Byron didn't dig deep enough. I've read parts of at least 5 Supreme Court rulings that defined for other purposes the Natural Born citizen as having both parents being US citizens at the time of birth. The purpose was clearly to prevent us from having a president with split loyalties or one with parents residing outside of the United States where a threat upon them could influence policy.
If Rubio doesn't qualify, he doesn't qualify. I think it much more important to stick to the Constitution than to nit pick at it to try and serve our own political purpose. As for the birthers, grow up. The birther argument is promoted by Obama's own people as a distraction. It's working. No one takes the citizen argument seriously because of it.