As Paul mentioned, medial shin splints are frequently (there is no 100%, right?) caused by overpronation placing stress in the medial side (inside) of your lower leg. Motion control shoes reduce your pronation, which reduces the stress to the medial side of your lower leg, which is the underlying cause of the medial shin splints.
Paul, if I’m oversimplifying or missing something, it sounds like I’m not nearly the expert on the topic that you are. Feel free to fill in the holes or start from scratch.