Briefly, Benjamin traces the phrase to English common law, back through Blackstone to the Magna Carta: Be you a 'natural born' subject... of the King. If so (and virtually all colonists were pre-Revolutionary War), then you were, barring being an American at 1789, not natural born. It was inserted last minute by John Jay to prevent a Royal post- 1789 from coming over and attempting to win election leading to a reunification with the British (Crown).
So dual citizenship may preclude BHO with possibly four dualities (UK, Kenyan, Indonesian and Canadian) even if he was born in Hawaii. Benjamin goes on with some humor pointing out that Gov. Richardson born in the States but of a native Mexican mother may be qualified to be both POTUS and POMexico.
One is natural-born according to the statutory requirements for citizenship-at-birth at the time of one’s birth. Dual citizenship, whether at birth or acquired later, does not preclude American-citizenship-at-birth.
The words in the Constitution may have had the purpose of excluding subjects of the King, but the words don’t say that that’s the only purpose.