The Medicare schedule is generally low because of the negotiating power of the Federal government so when Anthem (or whoever) says something like "we'll pay Medicare rates" or "we'll pay 120% of the Medicare rate" they're really just cutting payments and increasing patient costs. Nothing more.
In the recent BCBS case, all they were doing was saying "it may take 8 hours for the surgery but we're only going to pay you for 3". They haven't made the surgery cheaper to provide. They just wanted to pay out less.
Also, if we're going to simply do everything based on Medicare, why exactly do we even need private insurers? Just expand Medicare to everyone if the schedules are good, right?
You are exactly right that Anthem is demanding providers charge less for surgeries, not for surgeries to take less time. Providing "less anesthesia" is not a thing. This is entirely about preventing health providers from charging more money to Anthem and, in turn, their customers. That's why Medicare does the same thing.
This is about the trade association for anesthesiologists deputizing angry people on Twitter to go to bat for them overcharging for their services.
You cannot reasonably support Medicare and claim that Anthem was doing something unconscionable, because Anthem was adopting Medicare's own policies.
Medicare's admin cost ratio is a function of who it covers. Somewhere in the comment history on HN, there's a short writeup I did of how the math works out if you extend Medicare to the whole population; the admin overhead, for obvious reasons, shoots up --- people pay the same amount of money but require far fewer services, reversing the "advantage" Medicare has in the metric currently.