There are far too many incorrect points in that video to give him any credibility whatsoever. I'll just mention two from yesterday's memory, since I don't want to waste any more of my life watching it again.
1. His statement about head shots shows a lack of understanding about the dynamics of defensive situations. Anyone who's done any force on force training (or been in a violent encounter) knows from experience that delivering a head shot, under stress, when everyone is moving - is far from easy or certain.
2. His statement at the end about how you can't miss with a shotgun. Seriously? At typical defensive distances (say 21 ish ft and under), a shotgun must be aimed like any other gun. The shot spread is around 1-4" in that range - easy to miss. It's not a fire hose.
Noticed many such ignorant statements throughout the video, but I hope these suffice.
Agree with everything you said except, I suspect the majority of SD situations for the average person is going to be at home. With a distance of around 10 feet maybe. If we are talking SD out in the open so to speak, a shotgun is an impractical weapon to carry around. So the average person would not have a shotgun with them. Context should be considered. I believe the guy in the video was talking home defense, not roaming.