The vet most likely had good intentions. Some puppies fall outside the norm in reactivity and reactively biting hard is not normal in tiny pups especially when nothing for than petting is being done to them. Those are the ones that develop issues usually fear aggression if nothing is done.. I always discuss socialization and puppy classes and stress it with those puppies that are more reactive. Fear aggression is very common and extra time to carefully socialize, handle and train these pups is needed. Hopefulluy that is what the vet was trying to point out(although badly).
I have told 2 people in 12 yrs their dogs were going to be big problems that young. One was a 10 wk Husky. He was very calm(too calm),very watchful and just stood on the table and then exploded out and bit down with no bite inhibition. I was worrried about the lack of bite inhibition and the zero to all reaction. Suggested early and often socaialization and getting in a puppy class ASAP and going for minimum of 6 months straight and discussed training bite inhibition. They didn't go to any class and did nothing with the dog. By 5 months he could barely be handled for his neuter. At 9 months, He bit the 12yr daugther in the calf as she walked by. At 11 months, he bit a dog trainer in the chest. At 13 months, He bit the adult female owner in the forearm and wouldn't let go. She had 14-15 stitches. He was put down then.
The other a 7wk old white GSD, again no bite inhibititon(bit me 3 times on the forearm before I could move and drew blood-was standing on the table and I touched he shoulder), severe fear reaction(barking lunging ,snapping on the floor, on lead before visit). Talked about socialization handling, bite habition training and classes when old enough. Again owner ignored all advise. Put down at 16 months for severe fear aggression and severely biting the neighbor.