I have never seen a vet or tech put a dog on its side to examine, they do it while they are standing. They might put there hand gently around muzzle if the dog is panting. That would be acceptable, squeezing the muzzle is not. In the pups defense he had no where to go and what they did was make him feel pinned. Get another vet.
Misty- Samoyed Mix, Tannor- Golden Retriever CGC
Robyn- GSD CGC, TC, Midnite-GSD CGC,TC, Brennan-Golden Retriever CGC, Batman-Husky/Greyhound , Apollo-GSD