There is established case law precedent on the other side of the argument as well:
Mustata v. US Dept. of Justice, 179 F.3d 1017 (6th Cir. 1999) (children born in US to two Romanian citizens described as “natural born citizens” of the US):
Petitioners Marian and Lenuta Mustata are citizens of Romania. At the time of their petition, they resided in Michigan with their two minor children, who are natural born citizens of the United States.
DeTomaso v. McGinnis, 970 F2d 211 (7th Cir. 1992) (equating “natural born citizen” with “native born citizen” for purposes of presidential eligibility): “DeTomaso is ‘eligible’ to be President of the United States if he is “a natural born Citizen … [who has] attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.” Art. II § 1 cl. 5. A 35-year-old native does not have a property interest in the presidency.”
Diaz-Salazar v. INS, 700 F.2d 1156 (7th Cir. 1983) (child born in US to Mexican citizen is “natural born citizen” of US): “Petitioner, Sebastian Diaz-Salazar, entered the United States illegally [from Mexico] in 1974 and has been living and working in Chicago since that time. *** The relevant facts which have been placed before the INS, BIA, and this court can be summarized as follows: The petitioner has a wife and two children under the age of three in Chicago; the children are natural-born citizens of the United States.”
Nwankpa v. Kissinger, 376 F. Supp. 122 (M.D. Ala. 1974) (child born in US to two Biafra citizens described as “natural born citizen” of the US): “The Plaintiff was a native of Biafra, now a part of the Republic of Nigeria. His wife and two older children are also natives of that country, but his third child, a daughter, is a natural-born citizen of the United States.”
Liacakos v. Kennedy, 195 F. Supp. 630 (D.D.C. 1961) (holding that where evidence supported contention that person was born in US (to two citizens of Greece), he was a “natural born citizen” of the US): “The plaintiff claims that he is a natural-born citizen of the United States, having been born in Wheeling, West Virginia, on July 14, 1900. He claims that when he was two or three years of age his parents returned to their native Greece… ***
The Court is of the opinion that, weighing the evidence on both sides, the plaintiff has established by a fair preponderance of the evidence that he is a natural-born citizen of the United States, and the Court so finds.”
Nyman v. Erickson, 170 P. 546 (Wash. 1918) (child born in the US to Russian citizen was “natural born citizen” of US):
“Appellant was therefore, as correctly decided by the General Land Office and the Department of the Interior, not an heir of the deceased entryman, while at the time of the final proof at least the grandchild Esther Gustafson undoubtedly was. She was born in a state of the United States, and whether her parents were naturalized or not, under the Constitution she is a natural-born citizen of the United States entitled to the benefits of all the laws of the United States and of the state. U. S. Const. Amend. 14, § 1.”
State ex rel. Carroll v. Sup. Ct. of Washington, 193 P. 226 (Wash. 1920) (holding that there are two (and only two) paths to citizenship and that natural born citizenship depends upon location of birth): “According to the Fourteenth Amendment of the Constitution of the United States there are two methods by which a person may become a citizen: (a) By birth in the United States; and (b) by naturalization therein . A natural-born citizen’s right to vote depends upon his place of birth, and this is the fact to be established. A naturalized citizen’s right to vote depends, not upon his place of birth, but on a judgment or decree of a court of competent jurisdiction, declaring either him or his ancestor a naturalized citizen.”
If the argument comes from a dissenting opinion then it is not established case law precedent.
“Wong Kim Ark, ever since his birth, has had but one residence, to-wit, in California, within the United States, and has there resided, claiming to be a citizen of the United States, and has never lost or changed that residence, or gained or acquired another residence”
This was part of the opinion by Justice Gray. Obama had a foreign residence after his alleged birth in Hawaii. Seems to me if Ark had residence in Indonesia for several years would he kept the same opinion.
Chief Justice Waite said: “Allegiance and protection are, in this connection” (that is, in relation to citizenship),
reciprocal obligations. The one is a compensation for the other: allegiance for protection, and protection for allegiance. . . .
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 [p680] 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. For the purposes of this case, it is not necessary to solve these doubts.
It is sufficient for everything we have now to consider that all children born of citizen parents within the jurisdiction are themselves citizens.
Another remarkable example of ignorance is the Indiana Supreme Court decision stating that the U.S. had already knowingly validated the presidency of the son of a non-citizen, Chester Arthur. This was a complete fabrication, since Leo Donofrio discovered the fact of Arthur's father's naturalization date, when Arthur was 14, at the end of 2008. Donofrio searched the literature of the time for any hint that this was suspected, and only found the reference by scouring the few remaining private Chester Arthur papers, since Arthur had his records burned shortly before his death. Even Arthur's biographers had missed the significance of Arthur's father's naturalization date - but then they were not looking.
Of course no circuit court decision can alter supreme court precedent, accepted common law, as exemplified by John Marshall in 'The Venus 12 U.S. 253, 1814' citing Vattel and quoting the famous definition of natural born citizens, “...born in the country of parents who are its citizens.”