I just don't think the theory works. Most people develop stutters before they experience much social interaction and the brain changes so drastically over the first couple decades of life it's totally plausible that the structures of the brain related to stuttering change enough that the stutter goes away. It was years ago that I read this so I can't give you specifics but there was a study I read that imaged the brain of stutterers and it found that certain areas of the brain were measurably different from the norm and likely caused the stutter. It found that people who "grew out" of their stutter had that part of the brain strengthen its connections. I feel like it was still visibly different but I can't remember specifics. It seems really unlikely to me that anyone's stutter could be fully in their own head.