From the book In Search of Equality: The Chinese Struggle Against Discrimination in Nineteenth Century America by Charles J. Mc Clain
Page 363 footnote 4: “In a case decided 12 years later, Kwock Jan Fat v. White, 253 U.S. 454 (1920), the Supreme Court, following the principles laid down in Chin Yow, ordered a Chinese person admitted to the United States on the grounds that federal officials had disregarded evidence plainly relevant to his claim of citizenship. “It is better that many Chinese Immigrants be improperly admitted,” said the Court, “than one NATURAL BORN CITIZEN of the United States should be permanently excludd from his country.”
This doesn't help your argument. Kwock Jan Fat was a natural-born citizen under the same criteria defined in Minor v. Happersett:
[the petitioner] claimed that he was 18 years of age, was born at Monterey, California, was the son of Kwock Tuck Lee, then deceased, who was born in America of Chinese parents and had resided at Monterey for many years; that his mother at the time was living at Monterey, and that there were five children in the family, three girls and two boys.
Kwock Jan Fat was born to a father who was a 14th amendment citizen. IOW, Fat was a natural-born citizen because he was born in the country to a citizen father. This is not the case for Obama and not the case for Cruz.