I don't think it is analogous. The hamstring problem is a muscular problem. Short sprints would be more apt to tear the muscle if it is not probably warmed up or if there is cramping due to fatigue or dehydration. The distance runner does not have the violent muscle movement and even if he starts his exercise with cramping, he is more likely to warm up the muscle and feel better during his exercise than to injure himself. The shoulder is a joint with tendons, ligaments and muscle. I would imagine the theory is that working several times a week fatigues he muscles around the joint without adequate opportunity to recover. The fatigued muscles cannot hold the joint together as well as they would like and that can strees the ligaments etc.
Edit: That being said, I think it is not a bad move to put him back in the closer's role. We went from having a strong rotation to having a big question mark and 2 forty year olds. The bullpen is now fairly strong, but that could break down from overwork.