We've got the recruiting complaints here in AZ also, but it is not totally directed at the Private and/or Religious schools.
Most AZ school districts have "open enrollment" where a new freshman can attend any HS they want. Once they start at a HS, however, there are guidelines regarding transferring to different schools. Barring certain things, like moving to another school's attendance area, the athlete and parents have to apply to the state association for athletic eligibility.
There have been cases of a kid attending four different high schools in four years by his/her parents renting an apartment in the new schools area....