I understand that. The discussion was about their kids being born in the US. As far as the US Constitution goes, their kids are US citizens.
I don't think that is settled. Those kids belong to their parents, who don't belong here. And that is a far cry from freed slaves who were born here of parents who were born here or brought aginst there will. Those people were certainly "under the jurisdiction of" the US. First as property and then as free men.