Wong Kim Ark did not address the Constitutional term "natural-born citizen," even though it referred back to another Supreme Court decision, Minor v. Happersett, cynwoody. Wong Kim Ark was determined to be native born. Note the lack of the term "natural-born," here. They are not the same, under the Constitution and under the law.
The reference back to Minor v. Happersett does not support your contention, either:
"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. These were natives or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further, and include as citizens children born within the jurisdiction, without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
Under Happersett, a natural-born citizen is correctly clarified, via understanding of this term of art going back to Bingham, to the John Jay letters, and to Vattel's The Law Of Nations, to mean born citizen without a doubt. Doubt entered the picture due to Obama being born a British citizen under The British Nationality Act of 1948, in effect at the time of his birth. He cannot be, as a state of nature, considered a born citizen of the United States, when he was born British, transmitted to him by his father.
The term “natural-born citizen” is quoted and used in the Wong ruling. They cited other cases where the term was used, for example:
“In U. S. v. Rhodes (1866), Mr. Justice Swayne, sitting in the circuit court, said: ‘All persons born in the allegiance of the king are natural- born subjects, and all persons born in the allegiance of the United States are natural-born citizens. Birth and allegiance go together. Such is the rule of the common law, and it is the common law of this country, as well as of England.’ ‘We find no warrant for the opinion that this great principle of the common law has ever been changed in the United States. It has always obtained here with the same vigor, and subject only to the same exceptions, since as before the Revolution.’” United States v. Wong Kim Ark, 169 U.S. 649, 662-663 [cit. omitted.]
“Wong Kim Ark was determined to be native born. Note the lack of the term “natural-born,” here. They are not the same, under the Constitution and under the law.”
- Such a distinction has not been put in law nor is it in any SCOTUS rulings or accepted by any court.
Happersett quote: “These were natives or natural-born citizens” - showing that natural-born is synonymous with native-born in the eyes of the court.
“Some authorities go further, and include as citizens children born within the jurisdiction, without reference to the citizenship of their parents. “ - That’s what the Wong decision ruled on, saying 14th amendment meant just that. They removed the doubt on it.
Also, “doubt” does not enter into it when you have the possibility of dual nationality. See Perkins v Elg (a dual nationality does not cause you to lose natural-born US citizenship; you only lose your US citizenship by renouncing it).