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I have seen zero evidence that the actual, documented experiences of CHL holders (or SD experiences in general) bears out this thesis.
In fact, quite the opposite.

You noticed that too.
The only conclusion I can draw is one we should already have expected. Defenders with lowcapacity handguns who prevail against multiple attackers are NOT doing so by shooting all their attackers to the ground by making multiple solid hits on each one.
Clearly, what's happening is that one or more of the attackers is chosing to run rather than stand and fight. The Lance Thomas incident is a perfect example. Mr. Thomas, armed with a 5 shot handgun, prevailed against two attackersbut not because he applied 2 solid hits each. He won because the second attacker ran when the shooting started.
So, does that mean that capacity is meaningless? Not really. It was simply the luck of the draw that the second man ran. Had he stood and fought like his accomplice, Mr. Thomas would likely have not prevailed given that it took him 3 shots to neutralize his first opponent, leaving him only 2 to deal with the second.
Clearly there needs to be a balance.
Moving up in capacity obviously improves your odds, but you can't get carried away in that direction because it's not terribly likely that you'll be able to take advantage of a huge round count in the few seconds a gunfight typically lasts.
Improving the hit rate probability (sharpening shooting skills) clearly helps, but only if you have the capacity available to take advantage of it. For example, even a very impressive 70% hit rate only gives you a 53% chance of scoring 2 or more hits on each of 2 opponents if you're armed with a 5 shot handgun. On the other hand, if you can achieve just a 50% hit rate with a 9 shot handgun, your odds of success are 75%.
As with many things, it's a tradeoffa balance needs to be found.
Clearly these calculations don't tell the whole story. They only provide limited insight into certain aspects of a gunfight. That insight needs to be combined with other information before the big picture can start to take shape. But without that insight, a person can have a very mistaken impression about their chances against more than one
determined attacker.
Here are some plots that lay things out fairly well.
In this plot, each line traces out the probability of success with a given hit rate. So if you take the bottom line (10% hit rate) and trace across to where the bottom axis label reads 9 (# of shots), the height of the line will give you the probability of making 4 hits with 9 shots if your hit rate is 10%. It's a very small number...
In the plot below, each line traces out the probability of success with a given number of shots. So, if you take the bottom line (5 shot line) and trace across to where the bottom axis label (hit rate) reads 50%, the height of the line (about 20%) tells the probability of making 4 hits with 5 shots and a hit rate of 50%.