Her quote was foolish and plays into class war etc. she’ll know full well the embossed paper and polls are not every private school and the schools affected most will be the less prestigious smaller ones.
The likes of eton can charge what they want because of the very wealthy families but even somewhere like Cranleigh which is nearly as expensive is not passing on full vat. So there’s a good chance that the government won’t get as much money as projected as schools will not all pass on 20% and some will be able to claim back lots of money for capital projects.
Regardless of views on the policy, they were foolish and reckless to implement it mid-academic year in January without the guidance and detail to back it up now. Schools are having to make decisions re what to pass on without full guidance on the fiscal rules they’ll have to follow. They could have easily provided a transition period until next September that would have given much more stability and certainty to everyone - not least the state schools who’ll be getting new pupils mid academic year in greater numbers than normal.