I have to get up close and personal with and poke and prod dogs that are sick, in pain, stressed and nervous on a daily basis. In 18 years I have been seriously bitten once by a dog - a Yorkie (and quite a few times by cats, assorted small furry creatures and birds, birds are the worst!). I've encountered more who I know would have seriously bitten me given the chance. By 'seriously' I mean that the dog would attack with intent as opposed to giving a nip or a minor bite as a warning/through fear/in panic. These 'serious' dogs represent a tiny proportion of the thousands I have treated.
I can read canine body language extremely well and of course we use muzzles when necessary, but the vast majority of dogs have high to very high bite thresholds, meaning that they would have to be pushed to extreme levels to do anything more than give a vocal warning. Far, far more dogs are avoidant than confrontational when under stress/in pain etc., they want to get away, not to attack.
There are dogs for whom it is not in their nature to react under any circumstances I've ever seen - I've treated dogs of all sorts of breeds with horrific injuries and in extreme pain (RTAs, compound fractures, deglovings, burns etc.) who will let you lift/handle/manipulate them before they can be sedated, and during the course of ongoing treatment, with the most unbelievable tolerance and stoicism. Genuinely, as a whole, dogs are the most remarkable creatures.