What I said was the "theory" is that correspondence players are not capable of being good chess players without help. It's based in part on the belief that if you're not an OTB titled player, you're dirt.
I don't agree with this theory and as you know statistics can be manipulated until the result you want is obtained. The "methodology" used and benchmarks you cite (which are not really benchmarks but the opinions of some patzer amateur statisticians) can be fine tuned in several places to be more accurate (or alternatively to yield the results you want). It's all just someone's theory.
I believe cheating is a problem that needs to be addressed, and not just engine use but live chess lag cheats too. That said I don't believe the methods used on chess.com are 100% accurate. I have no doubt that clean players get banned, and cheaters missed.
Nor do I believe that all cheaters will be caught one day and we'll have a clean chess experience on this site.
But this thread was originally about the ratings cap - which I think is silly. You can't label someone a cheat because of their rating or acheivements or some 6 second puzzle, or the fact they don't have an OTB title. You have to evaluate their games in a fair and objective manner. I'm not sure such a method for evaluation exists.
I agree.
That's not what the rating cap does. It's to discourage cheaters not to punish strong players. If chess.com wanted to label them cheats they would have a mass banning of them all.
I agree. But the problem is the site is too big. There are too many games for the staff to sort though in a fair and objective way.
I think this is part of the reason the rating cap is being considered. There is no perfect method and there is no chess website 100% clean of cheaters. The rating cap isn't perfect and its not an instant solution, but I think it stands to do much more good than harm.

I flat out don't believe it. I'm starting to get worried about the detection methods on chess.com as it seems innocents are being banned. Again, I'm not paranoid, but I'm almost afraid to play sharp openings because of a false positive engine detection by chess.com. What I mean is that (although my corr. rating took a dive-bomb after withdrawing from a tournament because of having too many games to keep up with) I'm still somewhat scared of the thought that playing tactical forced lines could lead to account closure. What I mean is that if I play a 1500 in the Sicilian Dragon, and they make a bad mistake, I generally have a forced tactical win. My engine match-up for a game that would follow that pattern would be 100% (book lines, and then tactical sequence). I'm 99% sure that Fezzik wasn't cheating, and I'm very concerned about detection methods.
The detection method will ding you for "obvious" moves (forced escape from check, forced recaptures, only legal move and other obvious moves) because they will match the engine's 1st choice 100%. Of course some moves will be obvious to everyone, but the definition of obvious depends to some extent on the strength of the player you are evaluating, and the strength of the person doing the evaluation.
Playing forced tactical lines won't get you into trouble though, unless you're making moves that happen to be the #1, #2 or #3 choice of whatever engine is spying on your games more than about 60,70 or 80% of the time respectively.
Strong OTB GM's and strong correspondence players can exceed these percentages in a game or series of games but the "theory" behind the cheating methodology is that correspondence players are incapable of being good chess players without help. I'm not sure where that theory originated and I don't agree with it, but yes it's possible that innocent players can get busted by this method.
Right.
Not in any length and not against equal opposition.
This is why it takes many games to be banned using this method (note chess.com doesn't disclose it's detection method).
No past WC or pre-computer age CC player has ever exceeded the established benchmarks over a series of games simply because the benchmarks were set by these players themselves (and are surprisingly consistent throughout history).