I've never heard you couldn't and I know my parents went running there last month (and do every trip between various resorts). Are these "no pedestrians" rules posted? Do Disney police or security really stop people for it?
I tlaked to my parents and they were "yelled at" for running along the side of the road once. They've done it 'hundreds' of times and no one else ever said anyhting, INCLUDING the guards at the resort gates when they were entering or exiting... So, are you allowed to? Probably not. Do people do it? Yes.