The Supreme Court explicitly rejected this reasoning in Plyler v. Doe (1982).
> This Court's prior cases... cannot be distinguished on the asserted ground that persons who have entered the country illegally are not "within the jurisdiction" of a State even if they are present within its boundaries and subject to its laws. Nor do the logic and history of the Fourteenth Amendment support such a construction. Instead, use of the phrase "within its jurisdiction" confirms the understanding that the Fourteenth Amendment's protection extends to anyone, citizen or stranger, who is subject to the laws of a State, and reaches into every corner of a State's territory. Pp. 457 U. S. 210-216.
> This Court's prior cases... cannot be distinguished on the asserted ground that persons who have entered the country illegally are not "within the jurisdiction" of a State even if they are present within its boundaries and subject to its laws. Nor do the logic and history of the Fourteenth Amendment support such a construction. Instead, use of the phrase "within its jurisdiction" confirms the understanding that the Fourteenth Amendment's protection extends to anyone, citizen or stranger, who is subject to the laws of a State, and reaches into every corner of a State's territory. Pp. 457 U. S. 210-216.