After fostering 15 basenjis over the last 3 years, along with our own two, we've encountered a few biters (of varying degrees of seriousness).
First, we entered the crazy basenji world 3.5 years ago when my wife and I lost a screw or two and made an impulse buy of a tri at the local mall's pet shop (we paid penance for the sin of supporting the puppy mill industry by joining BRAT). He was a playful, sweet dog, but extremely food aggressive. Not knowing any better, I attempted to do an "alpha roll" on him. It only served to make him more resentful and distrusting. One time, he stole a pizza crust from my hand, and I foolishly attempted to take it away from his mouth. He ended up biting my thumb quite badly. This is while he was taking steroids for a skin reaction to a so-called natural-based dog shampoo.
Our first two fosters, a male and female were a pair that came at the same time. The female was very overweight, 40 lbs (no, that's not a typo). She was also acted very aggressively with our own two B's, but was not a human biter. Based on advice from our highly experienced BRAT regional coordinator, we had her tested for hypothyrodism. Sure enough, she came back positive for the condition, and we got her started on meds. Over a 4 month period, her attitude improved quite a bit, she lost 10 lbs, and her fur condition improved from being brittle and oily to soft and clean.
Because of this experience with the female foster, we tested our own 1-yr old tri for hypo. He was found to be hypo (most likely autoimmune type of hypo), which explained his weight and food aggressiveness. Once he got started on the meds, his behaviors & weight issue improved dramatically. He is a wonderful, sweet B who now can mostly regulate his food aggressiveness (but not his thievery behind my back).
Over the next 13 fosters, we tested those who demonstrated any signs potentially having hypothyroidism (which vary between dogs, but most common are aggressiveness towards other dogs and/or people especially over food, overweight or underweight, poor fur). Of the 17 basenjis we've fostered/owned, 5 were diagnosed with hypo, which is nearly a 30% incidence rate, suggesting that this condition is quite common in our beloved breed. The four fosters with hypo all improved quite dramatically after being started on meds.
5 of the 15 fosters were considered to be biters to varying degrees. 2 of them were diagnosed with hypo. We have found that biters tend to be such only in certain situations. Our latest foster is perhaps the worst of the 5 biters, and showed his aggression when someone approached him on the couch or massaged the top of his head. He has improved dramatically being on hypo meds, lots of love, patience, attention, and positive reinforcement training. He is a wonderful B, but just needed some special attention and medical help that most people are incapable of understanding or giving. Another biter would act aggressively, but when he attempted to bite, it would only be mouth pressure, no teeth pressure, so he clearly regulated his aggression to a point.
Another foster, who was sweet most of the time, could bite during a stressful situation. His current owner put him on melatonin supplements. We recently dog-sat him and couldn't believe how well-behaved he was.
The bottom line is that biting behaviors by some of the Bs can be attributed to a medical condition and/or being poorly/untrained by their humans, and/or a genetic influence. Usually, it's a combination of 2 or 3 of these issues. the key to treating biters is to rule out medical causes first, then implement a positive-reinforcement training regimen. Proper training will do wonders in helping such B's learn how to function properly in the "pack."