Oh boy. First of all, nobody who is just visiting and has no history with the dog should be trying to take food away from the resident dog…....any dog! That is just asking for trouble. Basenjis are not easily trained and are not known for obedience, but this can be overcome. Think of a cat disguised as a dog. You have to persuade them that the thing you want them to do is the thing they want to do. Basenjis respond well to clicker training (google it, lots of good info on line) and other positive methods. They don't respond well to positive punishment unless you really know what you are doing and have excellent timing. You may want to consult a Basenji savvy trainer if there is one in your area. These dogs are wonderful companions but they are not for everyone!
I think it is wonderful that you have rescued this dog from being put down, but you now need to do research on the breed, and this forum is a good place to start. Also, you may find this link useful:
http://www.basenjirescue.org/
Lots of Basenji information, and also if you find the dog is too much for you, perhaps you may want to rehome him. (BTW, do you know whose dog the Basenji was? I mean, did the girlfriend abandon the dog, or does she even know boyfriend was planning to get rid of him?)