No big deal? I have to say I wholeheartedly disagree there. Cheeks getting caught is pretty normal if your horse has a tight mouth- fleshy bits at the back just get in the way and its often unavoidable if you are going to do a proper job, however it should not be assumed you are definitely going to get caught- a really good vet/ EDT will try their damnedest not to! If your horses cheeks are severely caught and sore then this is another issue altogether- the first suggestion I have is that you find a BAEDT/ WWAED qualified dentist/ vet over an unqualified (dentistry wise) vet to take a look.
Canines should never EVER be flattened off to gum line EVER. Some horses have naturally small canines, but from your post it sounds like your horse has had some serious work done on these. Shortening canines can expose the pulp and lead to the tooth developing pulpitis or an infection/ abscess.
I cannot stress enough the importance of using a BAEDT/WWAED qualified dentist or at least a vet who has taken said qualification- those who hold such a qualification are trained and rigorously tested, along with continual development as a requirement of membership.