I got my "deckert's" ratsnake as a wee little hatchling and have handled him over the years. As a result, he is completely docile and even does well with groups of children when I do presentations at schools.
Anyhow, after returning from vacation once I reached in and grabbed him too quickly or something. He whipped around and bit me on the nose. I was absolutely stunned and even had to ask Tamara whether I'd really been bit. She told me that I had and to wipe the blood off my nose before it got on the carpet.
So yes, even the tame snakes have the potential to bite. They are fundementally instinct-driven.