What happens is that hospitals and other health care organizations negotiate a rate per procedure, not per patient. They look at how much it "should" cost, base

What happens is that hospitals and other health care organizations negotiate a rate per procedure, not per patient. They look at how much it "should" cost, based on materials and doctor's time. You can't go to an insurance company and say, "I know we negotiated a rate of X for this procedure, but the patient is poor, so I'd like to charge less for it." Well, you can, but the insurance company would come back with "Sorry, that's not in our agreement. X for procedure Y." Or worse: "So, you can actually charge less for procedure Y? In that case, we'd like you to charge that lesser rate anytime you perform that procedure, regardless of the wealth of the client."