The Supreme Court said, in essence, that those Secretaries of State were completely wrong about what “not subject to a foreign power” and “subject to the jurisdiction of the United States” actually meant. And if you read the history, the law, and the debates in Congress on the Civil Rights Act and 14th Amendment - the US Supreme Court was absolutely correct.
Here's what the Supreme Court actually said...
"The evident intention, and the necessary effect, of the submission of this case to the decision of the court upon the facts agreed by the parties were to present for determination the single question stated at the beginning of this opinion, namely, whether a child born in the United States, of parent 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. For the reasons above stated, this court is of opinion that the question must be answered in the affirmative."
In the cases I cited, both men had alien fathers who were not permanently domiciled in the U.S.