See my post at 231. You are misquoting the opinion!
No, I think you're misinterpreting what the Chief Justice is saying. Chief Justice Waite wrote, "At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also." He then noted that they were known as 'natural-born' citizens, distinguishing them from foreigners and the only other form of citizen; naturalized citizens. Nowhere does the Chief Justice define or imply a third class of citizenship, and in the quote in question he is clearly talking about natural-born citizens and those who define them one way as opposed to those who define them another.
But regardless, the Chief Justice is clearly not defining natural-born citizen as only those born in the U.S. of two citizen parents.