Be careful to avoid just trying out different methods of training and expecting immediate results - this can just confuse a dog (and its owner!). I personally, am in tune with the method suggested by Ivoss and the philosophy of NILIF. Of course methods can be combined (eg ttouch with hand feeding).
Watch carefully for warnings which may not necessarily be in the form of a growl. I've heard many people say that Basenjis bite without warning but this is not really true although the warnings may be very subtle.
I must say that although my Basenjis are taught to be amenable they do occasionally get over excited when out on the road but i just hold them out of the way until the adrenalin subsides.
In my opinion, you are doing very well with Basil despite your initial bad advice from the trainer. Have you managed to get a Basenji knowledgeable behaviorist yet?