Perhaps you are aware that Duncan v. Louisiana had dick-diddly to do with the question being natural born.
Also the snippet you quote is taken out of context. Perhaps you know that too.
Justice black said that its wiser to rely on what was said as opposed to relying on what was not said.
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"Professor Fairman's "history" relies very heavily on what was not said in the state legislatures that passed on the Fourteenth Amendment. Instead of relying on this kind of negative pregnant, my legislative experience has convinced me that it is far wiser to rely on what was said, and most importantly, said by the men who actually sponsored the Amendment in the Congress."
Also, Mr Bingham's quote is taken out of context and is also factually incorrect.
http://memory.loc.gov/ll/llcg/071/0300/03331291.tif
"I find no fault with the intriductory clause, which is simply what is written in the Constitution, that every human being born in the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution, a natural born citizen; but, sir, I may be allowed to say further, that I deny that the Congress of the United States ever had teh power or color of power to say that any man born within the jurisdiction of the United States not owing a foreign allegiance, is not and shall not be a citizen of the United States. Citizenship is a birthright, and neither the Congress nor teh States can justly or lawfully take it from him."
As we all know, it is not written in the Constitution, that every human being born in the United States of parents not owing allegiance to any foreign sovereignty is a natural born citizen.