My 8-year old son is also a nail biter. I used to be as well (wasn't hurting anyone but my own fingers) and stressful events would make it worse since I do have anxiety issues. I finally kicked the habit in college when I realized that the reason I kept getting colds/flu/sinus infections was because I was putting my fingers in my mouth after touching door handles, computer keyboards at the computer lab, etc. NASTY!! I was putting germs from every person who had touched that thing before me directly into my mouth!! I graduated to finger/hang nail picking since then. It's a nervous habit that most of the time, I don't even realize I'm doing (much like biting my fingers was. It certainly wasn't because my fingers tasted good or anything). I actually stopped all of it altogether once...and then I had final exams...I've been picking ever since.
I've been working with my son to help him be more aware of when he is biting his fingers and also helping him understand the whole germ side of sticking his fingers in his mouth. He's equally as grossed out and really is trying to be more aware so that he can break the habit on his own (with some little helpful "fingers out" reminders from us when we see him doing it). He's not scolded for biting. We don't fight him on it. In the grand scheme of things, it's really not that big of a deal and certainly not the worst thing he could be doing!
The bigger deal you make out of it, the more resistant he's going to be.
As a former nail biter, I grew up to be a productive member of society even though I bit my nails until I was 19 or 20 years old.