I recently did a test, 500mm + 1.4, tripod, mirror lockup, remote, IS on and off. I noticed that with IS on, no shaking was evident immediately following the shutter actuation, but there was with IS off. The images proved this to be true, also. According to some technical writers I've recently read, IS is also designed to eliminate or reduce vibration from mirror and or shutter motion.
Most of my wildlife images are taken at long distances, and any vibration reduction helps, since at 200-500 yards or more, the slightest vibration gets magnified considerably.
It may be true that at closer range, like when the subject is close to filling the frame, that turning IS off is acceptable. As the subject gets further away, IS gets more important.
Also, many times in the wild there is not time to swing around a tripod, get everything locked down in position and take the shot with mirror lockup and remote. IS is the answer. There might be time at a parade, though.