It's true in practice in a lot of places. In some places, persons without ironclad immigration status can be hassled out of enjoying public services with spitefully racist levels of bureaucratic process. It is similar to how same-sex marriages were denied after being declared legal by county clerks that refused to issue the documents that record their marriage publicly. The kids aren't denied public education, per se, but they certainly cannot get the same education experience as citizens and legal residents get. No electives. No extracurriculars. No field trips. No cafeteria payment accounts. All those things require the proper forms, and proof of residency, you see.

As a bonus (malus?), the very same malicious process can be used against kids of homeless parents.