There is a type of dog training technique called Positive Reinforcement training founded by Emily Larlham. You can find free limitless high quality training videos by her under Youtube channel, "Kikopup".
http://www.youtube.com/user/kikopup/videos?view=0
The concept of this training technique is getting the dog to WANT to do you what you the dog to do! Emily Larlham / kikopup features many training tutorials including tips and frequently asked questions. So if you have a question, there's a very high chance the answer is already posted somewhere else in her channel. There can be a multiple videos about one trick so watch out for those. Larlham is always adding more and more content and getting down to better organizing the information.
As far as how obedient basenjis can be. Here are some examples I found you can judge yourself:
http://www.youtube.com/watch?v=gUDPsUKLbtk&list=PL4DD6FA6A43484234&index=5
http://www.youtube.com/watch?v=bptDteozRbk&list=PL4DD6FA6A43484234&index=8
http://www.youtube.com/watch?v=FlMdQ3gklnc&list=PL4DD6FA6A43484234&index=16
http://www.youtube.com/watch?v=gwh0b7PLFQs
…I've also seen a video with impressive basenji obedience knowing a lot of vocabulary that is unlike any other that i've seen, but they took down the video 