Using half-eaten bones to make stock -- sanitary?
It's not sanitary, in the sense of following the health rules. Especially since it's unlikely that you're following the two-hour guidelines: the gnawed bones have been in the danger zone enough to potentially pick up an enterobacter that produced heat-stable toxins. Boiling will not fix that. And having been in somebody's mouth increases the chance that such bacteria is one that infects humans. 

Consider it this way: even if you're not squicked out by the basic concept, how would you feel if the bones had been left out on the plate for a day? A week?

As for whether it's safe, the short answer is "no". 

The odds it being actually dangerous are pretty low. The food safety rules are designed to keep the most at-risk people safe: small children, people with compromised immune systems, etc. Given how many other opportunities there are for food-borne infections to be picked up, I'd consider something that I picked up and simmered for many hours to be about as free from pathogens as anything I got out of the dirt, i.e. vegetables, which we often eat raw.

So I'll admit to having done it, but I wouldn't feed it to anybody except myself.