Right -- and a natural born citizen as well. One can be native born [soil] and not natural born [soil and parentage], but whoever is natural born [soil and parentage] is also native born. Young Steinkauler, by Vattel's definition, was both.
I don't think they did consider her parents citizenship status.
Sure they did. They noted that her father had been naturalized before her birth. Therefore she was both a native born citizen by birth on American soil and a natural born citizen because by birth on American soil and of American parentage. Elg was also both.
They quote approvingly of him being “native born” and that status allows him to run for President.
Unless they were being very sloppy, if they agreed with your concept, they should have said that he was both native born and natural born, and the latter allowed him to run for President.
It is possible for a court to write sloppy, but that normally isn’t assumed to be the case in a Supreme Court decision.
I agree with you about how it ought to be, but disagree with you on how I think a court will rule based on this decision. I also think no court will rule unless forced to by a carefully thought out case that leaves them no other option.