Don't be offend by what the Vet said, (yeah he probably could have worded it nicer but whatever - he go this point across without sugar coating it) it's his job to look after your animal and keep it healthy- it's also his job to keep himself healthy.
And yes maybe he was scared, especially if he thought your puppy was trying to bite rather than play.
If you've worked with animals for long enough you'll get hurt and it doesn't take much to knock a persons confidence - does that make them a bad Vet or a bad tech??
I don't think so, but iI do think it makes them more cautious. As long as they still do everything that needs to be done to examine the dog - but if that perhaps includes putting a muzzle on or in a sever case lightly sedating the dog that's fine - at least you'll get a thorough exam.
Off topic but it stood out to me:
I was surprised that some of you said you didn't have your dogs lay down in the exam room (on their side)
All my dogs have always been good about that, I just ask them to do a drop and then "dead dog" LOL and I actually practice restraining them by the legs and and laying them down (like the Vet - it's not hard there's a trick to it that won't hurt you or the dog and they get used to it really easily.
It's a good thing for them to know and may save a lot of stress at the Vet. When Hex was 4 month old and had leg surgery I got so many compliments on how easy he was to handle, lay down, pin down etc. they were treating another GSD puppy of the same age at thetime which they told me was a terror to deal with and had to be sedated for every bandage change etc.
He was and still is a mouthy dog and I do warn people that he will "nibbble" - when he went to see the specialist the Vet went to pet him and ended up with his hand in Hex's mouth - he had a bit of a surprised look on his face and just said 'oh you're a mouthy one " then laughed and went "typical GSD" LOL
I think us people often take offence way to easily and we just upset ourselves by doing so