I would
FREAK OUT! I have never tapped, smacked, hit, or bonked one of my dogs on the nose. In the past I have used *touch* to discipline my dogs (never my yorkies, I haven't had to). I used the touch correction as Caesar Millan teaches and I would tap them with a finger or two on the side of the body. I use it just to surprise them, and never to hurt them. This was always with my larger dogs (20-70lbs), and that would be a huge correction that I would only use if they were really misbehaving. If my vet were to be the first one to hit my dog, I would be extremely upset. A smack on the nose is completely inappropriate IMO, and I would be finding another vet pronto. There are other ways to correct a dog's behaviour, you'd hope that he would know that. Did your dog actually touch the vet with his teeth? Maybe in that instance I could see it, because you do need to match the intensity of the dog while correcting them, but still....what a way to make Rylie more fearful of the vet!
Please don't leave the forum. Just ignore the posts that ruffle your feathers and learn from the rest. YT is an invaluable resource.