This has recently worked for me. I would not say it is the gum that is the "cure", but I would say you are nailing it that it is a distraction and even more deeper it makes you not self-conscious. I think stutters put a lot of attention on their speech when they are talking and that's where most of the problems come from. Remember, from the movie "The Kings Speech" he had him listen to music so loud that he could not hear himself talk, yet when he recorded his voice when the music was so loud he was perfectly fluent because he could not hear himself talk. I think it all boils down to how self-conscious we are of our speech. When I read out loud to myself I don't stutter because I don't have to be conscious of my speech when I am all alone.