Thanks for the pointer to that book. When I search for "natural born," I find this:
After an exhaustive examination of the law, the [Lynch] court said that it entertained no doubt that every person born within the dominions and allegiance of the United States, whatever the situation of his parents, was a natural-born citizen; and added that this was the general understanding of the legal profession, and the universal impression of the public mind. The executive departments of our government have repeatedly affirmed this doctrine.That seems pretty clear to me. And I can't find anywhere in the book the "punchline" you quote, so I suspect that's not from van Dyne at all but from the blogger you link to.
look for the white pages 12 and 13 here scroll about half way down
http://naturalborncitizen.wordpress.com/category/uncategorized/
the Citizenship of the US is a treatise not an analysis it has tons of cases but they are not analyzed.