I think this a flawed analysis of the economics of the situation. The entity benefiting here is the school, by avoiding having to pay for email hosting. That Google gets paid (in cash or otherwise) for providing that service is not surprising, and not at all analogous to hiring an independent contractor.

IANAL, but it seems to me the important consideration here is who has duty of care regarding the students, and it's seems clear that it's the school.

Now, if Google lied regarding the scanning, the complaint may be valid, but that's a different argument.