Single Action. Double Standard

I was watching the Defensive Revolver Fundamentals video made by Rob Pincus and Grant Cunningham. One thing that bothered me was the admonition to only use a revolver in double action. I get that if I cock a revolver it has a short, light trigger. If I thumb off the safety on a 1911 is also has a short, light trigger. So why is a revolver more likely to have an negligent discharge than a 1911? I understand there are benefits to double action such as shooting faster. With a little practice is it plenty accurate enough to stop a man sized attacker at surprising distances. That still doesn't explain why a single action only pistol like the 1911 is considered safe but a cocked revolver is an accident waiting happen.

One "explanation" I've been offered is that having two different trigger pulls is a bad idea. That, however, brings into question the DA/SA autoloaders. If switching between double action and single action is so perilous on a revolver why is it less so on an autoloader like the Sig P220, Ruger P95 or Beretta 92?

Single action with an autoloader == good.

Double action/single action with an autoloader == good.

Double action/single action with a revolver == Oh my gawd! Are you out of your mind?

Doesn't make a lot of sense.