Say two people get their appendix out and the hospital bill is about 15K. One person is uninsured, so they get a bill for the full amount. The other is insured, so their insurance company gets a bill for 15K. The insurance company has an existing agreement with the hospital and says "We're only going to pay 12K" and that's what the hospital gets. Then they pass on the 30 percent of 12K to the patient and get that. This is seen as a bonus the insurance companies provide - negotiating better prices - 12K vs 15K. But what's really happening is the hospital is going to try to get 3K more from the uninsured guy.
My argument (how I think it should be) is that the hospital has to demand the same payment from everyone for that procedure - you will be responsible for whatever portion your insurance company doesn't pay, which is full price for the uninsured. Now the other hospital across town is free to offer the same procedure for 13K or 8K or 25K - whatever they think they can get, but they have to charge that price to all patients. This promotes competition between providers AND insurance companies and it will result in lower prices for both.
I tried to clarify - different doctors are free to charge different rates for a given service (say 15K for an appendectomy), to make them charge the same is price fixing and should not be allowed. What I advocate is that Alice, Bob, and Charlie all get charged the same price by Dr. Sam regardless of insurance coverage or any of the other deals that take place today. Dr Alfred is free to charge a completely different price than Dr Sam.