Yeah, unfortunately what CMS pays for procedures bears little relation as to what private insurers pay. It all depends on the local market for the provider. If most of the population goes to only a few providers, the providers have a lot of sway in negotiations. They will often ask for (and get) per-diem rates or percentage of charge.
If the population goes to a number of different providers, then the insurance company can play hardball and say "if you don't take this rate, you're out of our network, good luck with that". In those cases, they'll negotiate an MS-DRG + X% rate.
The reason why negotiated rates with private insurers are non-public is because it's a negotiating tool. If hospital A gets paid $5K for a heart attack and finds out hospital B a block away gets paid $7K for the same thing, the next round of negotiations will be very rowdy.