The reason IS/VR should be turned off on a tripod, is signal feedback that builds up in the system and causes the mechanism to move when it shouldn't. Some lenses are very prone to this, like the earlier Canon-L teles eg 100-400L, where the image can drift all over the place on a tripod. Lenses with tripod-sensing are usually okay, but even then it's a bit like stopping at the traffic lights and keeping the car in gear with the clutch depressed, as opposed to putting it in neutral with the handbrake on.
My simple rule of thumb, if I have a hand on the camera (eg subject tracking on a tripod, or using a monopod) IS stays on. If not, then switch off regardless.