Food allergies (especially nuts) are really a case by case basis. It really depends on the severtity of the allergy. If there has ever been a history of anaphylaxis (allergic reaction that involves the complete body, or the mouth, throat or lungs) it will be a disqualification and the chances of a waiver is very low. If there was only a one time episode, and he has had walnuts since then with no problems, it still may be a disqualification (this one falls into the "history of" catagory) but a waiver is much more likely.
Any time there has been an anaphylactic reaction requiring emergency treatment or an epi-pen was prescribed the chances of a waiver go down dramatically.
I'm not trying to sound like a doomsayer, I just want you to be aware of what the standards are, and what DoDMERB is looking for. If a disqualification is issued, and this is what your son wants, I would definately tell him to pursue the waiver.
I hope this helps, if not let me know and I'll see what I can do to help you.