I interpret this as meaning they are still citizens of Mexico and therefore not subject to our jurisdiction. If they have not sworn an oath to the US then they are still citizens (illegally resident in our country) of Mexico (or wherever) not US citizens. Amnesty may redefine that to mean we have made them subjects. A child born to a foreign national is still a foreign national.
Tell that to the California Welfare department and California Department of Education....I would suspect others in here from California can back me up on these goings on. As late as a year ago I would have conversations with my family and friends in So. Cal where I grew up about this happening. Granted, it's not like it's hundreds of people daily, but paying for schooling & welfare of one illegal's child because they ran across the border at moment of delivery is charity too much. The buck has to stop somewhere.