Burring is the same as filing, to what I understand. Also, I will note explicitly that rabbit teeth do grow naturally towards the sides of the mouth and inward to the tongue — that is not unusual, as that is how their teeth are designed. It typically is not a problem because the rabbit is chewing on wood and hay, which keeps them filed down. For rabbits who for one reason or another cannot maintain the teeth on their own, vets must intervene to file them for them. What the old vet was doing is what the new vet will do, which is filing the back teeth. That’s what it sounds like to me.
In terms of ethicality, in my eyes, as long as your rabbit is doing well, can recover well, and has a life worth living, I don’t see it as an issue. I would make sure that when you do schedule a filing, it is actually needed.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.