At my house Jet the try-ing has the longest coat. It's fairly soft and not so prickly when you pet him backwards. Digital the brindlewonderkid has a short harsh coat and it is definately prickly. His coat will make me itch and my skin will break out in red dots if it's been more than 3 weeks since he's had a bath. More so in the summer than winter. Zest the superstar in training (r/w female) has a nice short and soft coat and she does not make me itch. I like her coat best, but I don't think the others have an incorrect coat.
And I should clarify, that by "soft" I do not mean a texture similar to some other breeds or the soft texture of undercoats found in other breeds. Jet and Zest's coats are still "hard" enough to repell seeds, burrs and weeds. Most soft coats and undercoats collect that stuff like crazy. I had my hands on a poodle puppy yesterday. Gorgeous thick soft, soft coat; felt closer to rabbit fur than basenji fur. Way softer than any basenji coat. The coat absorbed the light rather than reflected it.
I did have a foster b/w basenji female that came to me with icky thin harsh coat and after being in my house and eating quality food, her coat became thick and really soft. Soft almost like that poodle puppy's. A little sleeker than that poodle's but it was a coat that I'm not sure would repel burrs, weeds, seeds. It would seem that a coat of that texture would be incorrect for a basenji. (but it felt really nice!)