Let's entertain the idea that "stuttering has to do with a speech control nerve." With your suspicion in mind, how would you explain people who learn to speak, develop a stutter at roughly age 3 or 4, continue as a severe stutterer until roughly age 26, then achieve fluency via speech therapy? Or that the first time consuming alcohol in my teens, I achieved perfect fluency for a few hours. But subsequent drinking sessions didn't provide the same increase in fluency.