Yeah, I would say bite inhibition training is "complete' at the puppy stage when they stop chewing on you in play. But you won't really know how complete it is as an adult until the dog might be forced into a situation where it really wants to bite either out of fear, or anger. Ideally, the dog would go thru a progression of 'bite' stages starting with an air snap, and then a muzzle punch (where it feels like the dog bit you, but there isn't any teeth marks or blood), and then a there is a bite where the dog opens its mouth and applies pressure, but doesn't break the skin. The idea is that the dog only applies as much pressure as needed in an emergency (in the dog's mind). A dog with no bite inhibition will overreact and inflict multiple skin breaking bites for someone bumping him while sleeping.
That is a worst case scenario, obviously. Lots of dogs wouldn't dream of biting a person; but the idea is to teach a dog how hard is too hard, rather than teaching them to never put their mouth on someone. And, as Robyn mentioned, singleton puppies, or puppies that were removed from their dam and littermates too early often have more trouble learning this.