Could it be that it forces you to focus on your speech motor skills? For me, when I’m focused on my speech, I don’t stutter. But it’s hard to direct that focus. When I talk about my stuttering I don’t stutter. My speech therapist couldn’t help me because the moment I walked into her office, I stopped stuttering, but when I was outside, I couldn’t speak two words without stuttering. Putting your thumb between your teeth makes speaking a more conscious task, giving you more control of your motor skills.