For starters, I'm just going to accept his muzzle energy figures as given, although at 1910 feet per second, he's probably talking about .22 WMR and not .22lr. No matter, though.
But his argument still doesn't make sense. He lists the muzzle energies for all three, and a 'threshold' to fracture the skull (that I've never seen before, but whatever). All three rounds surpass the threshold - so far so good. But then he's making the leap that the lowest-energy round will do the most damage?
If any of those three calibers are enough to fracture the skull, then you're either going to have a 9mm bullet, a .22 bullet, or a .45 bullet penetrating brain tissue. I don't think you can make a good argument that it's going to be the .22 doing the most damage.
EDIT - And even with the higher velocity, both the 9mm and .45 ACP still beat out the .22 in terms of muzzle energy (which greatly favors velocity over mass). So even if he's trying to go with the "energy dump" theory, the .22 is still the loser out of the bunch.