Yes everyone studies the same... And although there is a reputation amongst the NHS for poor physio's it is unique to each physio. You get good ones and bad ones. they don't have to be public or private. And that variance is in every profession.
If you are getting better than stick with the physio. But if you aren't and they aren't interested in finding out why and cannot explain to you why then thats when it's a good idea to see a different physio. - You need to have confidence in your physio or your rehab won't go well.
Pudding