I think that if that kid is born in the US, he/she is American and should have all the benefits and responsibilities that any American has. If the kid is not a US citizen, he/she should either be deported (after a court order) or issued a visa, depending on individual circumstances. There is nothing wrong with education of non-US citizens, there are plenty of exchange programs run by schools and universities.
If the kid is American, but his/her parents are illigal immigrants, they should be deported.