The first time I heard the theory that activity in the right (non-language) hemisphere was interfering with the smooth flow of speech in the left (language) hemisphere was in the early 1970's. Interesting to see it proved out almost 5 decades later. Also, in general, one of the jobs of the right hemisphere is to reduce activity in both hemispheres, so this fits in as well.....
Scientists at the Max Planck Institute for Human Cognitive and Brain Sciences (MPI CBS) in Leipzig and at the University Medical Center Göttingen have now gained crucial insights: The hyperactivity in regions of the right hemisphere seems to be central for stuttering: “Parts of the right inferior frontal gyrus (IFG) are particularly active when we stop actions, such as hand or speech movements”, says Nicole Neef, neuroscientist at MPI CBS and first author of the new study. “If this region is overactive, it hinders other brain areas that are involved in the initiation and termination of movements. In people who stutter, the brain regions that are responsible for speech movements are particularly affected.”