I always thought it was the opposite based on bills I received. When I payed cash with no insurance it was about a 50% "discount". When they know that insurance is paying for it and they will for sure get the money it seems to generally be more.
I guess it might depend where you are.
If a doctor agrees to accept certain insurance he usually agrees to accept what the company pays.
For example, the doc bills Blue Cross/Blue Shield $1,000 and BC/BS knocks it down to $400. Some dentists charge more than your insurance will pay and they bill you for the difference.
You'd have to work out a discount personally with the doc if you don't have health ins. Some docs will do it. Some will not.
Hospitals won't dicker with you. They just send you a bill with what they charge.