I don't think you should be put off just because of problems with your previous Basenji. He could, as others have said, have had a physical problem. Get your new Basenji from a reputable breeder and then make sure that you socialise him/her well and make sure that he/she encounters as many different environments as possible. Good socialisation is the key to many issues. You will, having had problems have been made more aware. There is much advice on this forum on dealing with various issues. If your breeder is conscientious and experienced he/she will be available at all times with good advice and will be able to guide you through any problemsd that may arise.
Much of the behaviour Jess mentions is due to the owners and not their Basenjis. There have been temperament issues in the past but mainly due to lack of intimate knowledge of the breed. It is rarely (apart from physical problems) due to the actual dog (although there have been instances). In the early days people had had little experience and treated them as 'just a dog' which Basenjis are most definitely not!
I'm sure Shelley will agree that her earlier experiences with a 'difficult' Basenji have helped no end in the way she has brought up her present two. I would also caution Shelley when she is told that dogs in the pedigree of her first Basenji were of doubtful temperaments. The first question I'd ask is whether the person who told her this was actually the breeder of the dogs mentioned.