jurisdiction n the power, right, or authority to interpret and apply the law : the limits or territory within which authority may be exercised
Illegal parents, I would expect, can be shown to not be "subject to the jurisdiction thereof". Children are subject to their parents; would this also place them outside of the "jurisdiction thereof"?
yes, people that argue that babies born here are citizens via the Constitution are wrong. It was another bad Supreme Court decision that has put us in this mess.