I too have had, and do still have one, and have competed in obedience with them.
Yes they are intelligent in lots of ways but not intelligent enough to disobey if necessary. I was once told by a BC enthusiast and expert trainer who also had a Basenji that if told to do so a Border Collie would jump off a cliff but a Basenji would say "Are you mad?".
When we used to train our collies one of our then basenjis learnt the obedience moves merely from watching us and the collies. She competed in matches with some very trainable breeds and never disgraced herself. The only thing she refused was to do the 'Fetch'. She would just turn and say 'You threw it, you go and get it!'