I would certainly excuse a puppy for taking off with a prohibited item, but by the time the dog is an adult it should have a good understanding of "no". "Keep away" is a game I refuse to play and there are consequences for absconding with "illegal" items. For the dog's own safety I make it clear what is legal to play with and what is not, and I reserve a stern "no" for occasions when it is needed. If this is a frequent problem, let her drag a leash and take immediate action if she grabs something she should not have. I dislike using the "trade" approach because a smart dog (which Basenjis certainly are) will learn that taking something you don't want them to have will lead to a reward. (otherwise known as "chaining" when you are trying to train a behaviour).
The most important thing is to refrain from rewarding the behaviour.....which means don't play her game and don't reinforce with your amusement, which will be apparent to your dog.