Okay I have taken a few deep breaths… and now going to weigh in.
That you took her response as rude and jumped into defending the trainer gives me an idea nothing anyone says unless it is in line with what you want to hear is going to get any consideration. So in my best Dr Phil tone... I'd like to ask... how's that working for you so far?
I don't have issues with prong collars and dogs that need something to give you a better handle.. say .. 100 pound plus dogs. But it is a tool, not a general training device, for leash walking. I don't care how many people this person trains dogs for, that doesn't make them good, or a good fit for your dog. Ceasar Milan has a following and he is an abusive dangerous person. Sadly, most people who need trainers do because they don't understand training... so they can't really tell if what is happening is right. I am begging you to read some of the books suggested.
Basenjis are smart. You train punitively, and they will take you on or shut down. You say you don't like treats as you don't want a fat dog... and you can take this as rudely as you like, but that's just utterly silly! You don't give a huge amt of treat! You can give TINY treats, low fat treats, anything and cut back a bit on meals to compensate. If you go with clicker training, you can eventually remove treats and just use the clicker noise. Good training, whether it is your child, dog, goldfish, rabbit, horse or whatever--you get results when you understand what motivates them and USE IT TO YOUR ADVANTAGE. Most dogs are motivated by food. Be smart, use it.
Get back to basics. Pretend the dog just came. Nothing in life is free is the way to start. No bed, period. Let sleep in a crate in the same room or on floor, but bed is off until all this is solidly taken care of. Some dogs can NEVER have bed privileges because it triggers bad behaviors. I am happy to say so far in my life only one dog fit that for me, but from 18 mos til he died, if he got on the bed, his lip came up.
Get a good basket muzzle and use it for nail clipping if you have to, but also work on retraining. http://www.clickerlessons.com/nails.htm
You said healthy.. but what blood work has been done. As pointed out, thyroid can cause some aggressive behaviors. Hopefully it is fine and what you are seeing is a dog maturing and really testing his limits. How you respond is going to set your life with him. Make this into a matter of domination instead of training and it won't go well. And that, not rudeness, is what folks were trying to say. I hope you step back, start at the beginning and reread in that spirit. It is truly a waste to come for help with folks like Pat who are overflowing with knowledge and experience and ignore them, depending instead on someone who may or may not have a CLUE about this breed and who seemingly imagines that you have to train hard for hard dogs… when the opposite is proved in training all the time. The positive trainer can get any dog to do more and better than the force trainer every single time. I suggest to you that any dog that cannot be trained in a positive way is probably unstable and not pet material. Positive may take a bit longer.. but it works, it works better, it makes your relationship with your dog better.
http://k9deb.com/nilif.htm a good rundown of Nothing in Life is free.
I'm not a fan of them. When I see someone walking a dog that wears a prong collar, all I think about is whether the owner is substituting a prong collar for well directed training. 
