Funny thing though, the courts seemingly had no doubts in 1847.
BARRY v. MERCEIN, 46 U.S. 103 (1847)
4. The plaintiff in error being of legeance to the crown of England, his child, though born in the United States during its father's temporary residence therein,-twenty-two months and twenty days,-notwithstanding its mother be an American citizen, is not a citizen of the United States.
I wonder where the doubts crept in?
You're quoting the Plaintiff's argument, not an opinion of the Court.
On the part of the plaintiff? Who knows? John Barry, the plaintiff in error, did contend that his daughter was not a citizen of the U.S. But the court did not rule that, nor did Chief Justice Taney make reference to the citizenship matter when he ruled against Mr. Barry and dismissed the case. So if there were doubts on the part of the court they didn't say so. In fact, since part of Mr. Barry's unsuccessful appeal was the claim his daughter was not a citizen, it might be said that the court disagreed with him in that as well as the other points of his case.