I agree with everything posted so far. To answer your question, Ivy hasn't bitten anyone in some years now (frantically knocking on wood). And she has always been fairly well behaved at the vet, but I always muzzle her for blood draw, and hold her head during shots. She tends to jump and scream bloody murder when they try to draw blood, so for the tech's comfort I muzzle her right away. She doesn't love it, but it is all done calmly, and we get through it.
Her temperament is one of the reasons why she wasn't bred, and the fact that there was quite a bit of Fanconi around her in her pedigree (this was prior to the test, knew that her mom was a carrier and her dad was at best a carrier, he died by car prior to becoming old enough to develop fanconi).
Her temperament IS why we stopped showing her for the most part. She didn't enjoy showing, and it wasn't that important to us to continue trying to rehab her for show.
So, it might not be horrible advice to have Denver neutered if he really does have issues with strangers, not just vets. But I don't know that it is a necessity…have you talked to his breeder?
And I think it is a little ridiculous to suggest euthing a dog that is loving with his family, because he is terrified of vets. You can definitely work through this. It is a matter of desensitizing him to being touched, and approaching strangers. It will take some work, and he will never be like a lab but you can definitely work through it. Try the book "Click to Calm" by Emma Parsons.
Like the others suggested try to find a vet that is understanding about dog behavior. And then you work with them to help keep them safe, and they will love you for it
Hang in there!