I disagree with this and so do police reports. One will kill someone just as dead as another but self defense is not about killing the person posing a threat, it is about stopping them quickly. There is a big difference in the amount of damage done by a hollow point at high velocity and a fmj at low velocity. This really isn't even debatable. I agree that shot placement is the biggest factor but some rounds absolutely do more damage than others.
I worked as an LEO for two different departments. No police report I've seen goes into any detail on the exact cause of death, or the reason for stopping, if death did not occur. Sorry, but it's not in the scope of any LE agency to figure out what made the stop...it's a medical issue, and the department defers to medical personnel for the answer.
As for comparing your rounds, its true a small FMJ will do less damage than a large, hunting JHP at twice the velocity. This was not part of the issue at hand, so you are correct...it's not debatable in this context. It can be said that a good, solid hit in a vital area with a .32 FMJ is superior to a non-vital strike with a .44 Spl JHP. That's another issue altogether. In the context of the issue at hand, a 9mm JHP made cheaply by Winchester in their USA bulk line will work as well as a .45 ACP Gold Dot, WIN Ranger, or any other round that is known as premium. Again, human A&P, medical science, and everything else observed about shootings since shootings began prove this. Police reports do not even touch this.
Yes, it is about stopping someone quickly, but any stop NOT created by the round disabling the subject physically is a psychological stop, created by the person's lack of will power to continue. When people do not give up, due to drugs, rage, etc., you see these cases on the news. They are the ones who take magazines full of ammo (of all calibers) before they quit. It's all a HUGE gamble on someone's part to think people will quit attacking when shot, because you have no idea who you are fighting, and what they are capable of doing.
Look up (to the extent you can) actual cases where it was determined how the shot ended the fight. You will see it is totally independent of caliber, power, etc. It is almost always related to direct tissue destruction caused by the main path of the bullet. Those other effects, such as cavitation, are secondary wounding factors, and will cause damage that is realized over time, but not immediately. IOW, the large rounds might cause incapacitation faster than smaller ones, but it will take a long time...time you don't have.