I would contest this statement on two grounds:

1. VAT is paid by the client/customer and collected by the business (school in this case) who passes it to HMG.

2. As a general principle I would regard it as a good thing if profits are reinvested in the business whether that business is education or any other activity.

That is not to say that I disagree with the idea of all those rich parents having VAT added to those fees!