There are different types of naturalization: individual and collective; voluntary and involuntary. Obama, for example, IF he can legally prove he was born in Hawaii would fall under involuntary, collective naturalization.
Of course, they don’t. Because they are the other kind of citizen, of which there are only two kinds in the law.
The key is "in the law." Natural-born means "without law" ... it is a type of citizenship that does NOT depend on law to make it so. This is what the court explained in Minor v. Happersett. Natural-born also means "without doubt." Other types of citizens at birth come WITH doubts that must be resolved: whether a law or constitutional amendment applies; whether the place of birth qualifies under U.S. law (such as through collective naturalization); whether a child was born subject to the jurisdiction of the United States (which the SCOTUS said in Wong Kim Ark is based on the parents having permanent residence and domicil); whether a child born outside the U.S. meets the residency requirements for himself or his parents; or whether other statutory definitions are satisfied, etc. With natural-born citizens, there's no need to satisfy a subject clause or statutory definition: born in the country to citizen parents is simple, authoritative, universal and with no doubts.
Except the law doesn’t require citizen parents. I think it should, and clearly lots of people on this thread think it should, but it doesn’t. If Rubio ever does decide to run, he could lawfully do so. That’s just how it is, and no amount of hyperbole is going to change it.
I’d like to see a citizen-parent requirement, not so much for candidacy rules but to finally deal more effectively with the anchor-baby problem. I don’t think the founders ever contemplated such an issue at the time. The founders were trying to stop any immigrant, after the revolution, from becoming President. Their concern was that the King of England might send agents to immigrate to the U.S. to try to become President— effectively nullifying the revolution. So they said immigrants can’t run.
That’s all this is about.