They are citizens - born in the United States per the Fourteenth.
Although Administrative Due Process has something to do with the Constitution, there also these cracks in the practice of administering laws that somebody has to fill with something ~ which tells you something very important here ~ that INS pulls it out of the old ying/yang on important matters more times than most people can imagine.
Give you a better example ~ Congress passes a law that says A, B, & C, when they occur, must be so and so. The President signs the law. The reg writers in the affected agency write "IF A, do so and so, whereas if B, do so and so, and if C ~ either with A or B, or exclusive there of, do so and so, but in all other cases do something else.'
I"ve had to write hundreds of rules to do exactly that ~ "something else" that wasn't imagined in the original regulatory formulation (From the Postal Rate Commission) or the statutes debated and passed by Congress.
That 'something else' shows up in the absence of the practical reality that D happens as does E and F and G, and even when A, B, and C rarely happen.
The rule gets signed off on, published in the federal register, and now it's law ~ DO D E F G ~ never contemplated, become the gold standard for all decisions in that area.
INS Has done the same with the citizenship clause ~ it was written to turn American slaves into citizens but it's being used for 'something else' ~ and without legislation! This just came into being! There's no emabling legislation. The law cases that seem to impinge on it relate to people who were born here to lawful immigrants!