I have a Basenji from a BYB. He's a wonderful dog and I love him dearly, but he has Fanconi. The test wasn't available when I got my dog, but it is available now, and I wouldn't buy a dog from ANYONE who didn't healthtest their dogs. I believe the test costs $65, and if they aren't willing to spend that to test each of the parents to make sure they don't spread this dreadful disease, then that is a breeder that cares only about themselves and how much money they can make at others' expense.
A lot of BYB Basenjis are Fanconi afflicted. The same dogs are bred over and over, year after year, which puts hundreds of dogs and their new owners at risk. Having lived with a Fanconi dog, I can tell you that it is NOT something that you want to risk, if you have any choice at all. My dog takes 14 pills a day, plus other meds sprinkled on his food. He is on a special diet, and I have to cook for him. He drinks a pitcher of water a day, which means he has to go outside about every two hours. If you don't watch him, he will gulp the entire bowl of water, then regurgitate it.
He has to have a full blood panel and venous blood gases taken every 6-8 months, and I have to drive to the university vet hospital to have this done, because it requires a special machine. He is prone to UTIs, pancreatitis, seizures and infections-- all of which he has had. He has a weakened immune system, and I have to watch every single thing that goes into his body. His vet bills are more than $1000 a year, and I have been doing this for more than seven years. And I am one of the lucky ones. The unlucky ones either lose their dogs early or simply don't have the resources to care for a special needs dog.
It would be far, far simpler, cheaper and better to just buy a Basenji from a reputable breeder. If I had it to do over again, I would. And next time, I will.
I hope you find the right Basenji for you! (And sorry, Petra, for usurping your soapbox.)