I have to admit some rats do bite but the vast majority of tame pet rats don't and would never dream of it, even when in a lot of pain.
Of the very few who do bite, some of them will nip if they think you are food, which is easily solved, some just don't like your fingers sticking through bars, some of them will bite if you surprise them suddenly or to protect their babies, and a tiny number are just nasty (I've had one rat who was untrainable; would run over to bite you
) but I've had a lot of rats and almost all of them I would have happily agreed to give you a thousand quid if they bit you.