Your quote from Wong Kim Ark does not say what you claim it does. The phrase it uses is “natural born subject.” It uses that phrase for the very good reason that it’s not ruling (making a precedential holding) about US law, rather is making a dictum about British law (about which it has no authority to rule precedentially.)
The government went on to ask:
“Are Chinese children born in this country to share with the descendants of the patriots of the American Revolution the exalted qualification of being eligible to the Presidency of the nation, conferred by the Constitution in recognition of the importance and dignity of citizenship by birth? (p. 34).
http://www.scribd.com/doc/23965360/Wong-Kim-Ark-US-v-169-US-649-1898-Appellants-Brief-USA
The majority opinion in Wong did go on to say: “’Subject’ and ‘citizen’ are, in a degree, convertible terms as applied to natives; and though the term ‘citizen’ seems to be appropriate to republican freemen, yet we are, equally with the inhabitants of all other countries, ’subjects,’ for we are equally bound by allegiance and subjection to the government and law of the land.’”
The question presented by the record is whether a child born in the United States, of parents of Chinese descent, who, at the time of his birth, are subjects of the Emperor of China, but have a permanent domicil and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the Emperor of China, becomes at the time of his birth a citizen of the United States by virtue of the first clause of the Fourteenth Amendment of the Constitution
The Court very correctly continues by never once uttering the phrase "natural born citizen" anywhere in the opinion.