I’m sure there are a lot of US-born parents fraudulently “stealing” seats in certain public schools which their children don’t have the right to attend.
The “caregiver affidavit” is widely used for this. Especially for grandparents’ homes, which are often located in a better school attendance area than the parents can afford.
For example, I’ve witnessed a family name a “grandparent” as a “caregiver” for their kids to attend a certain elementary school and had them sign the affidavit. But the signer was actually was a “great grandparent” who was using a walker (couldn’t drive) and had a caregiver themselves!
This 89-year old couldn’t possibly pick up these children from school, make them lunch or snacks or do anything for these kids. Her great-grandchildren never stayed with her after school but simply used her address for enrollment and mail purposes.
So, yes, today parents (US born or otherwise) will do anything to get their kids enrolled in what they perceive is a “better” public school than the one they have a right to attend.