No they don't. Hospitals mark up for people paying cash. This is because they know most of the people paying cash won't pay at all. The markup for people paying cash is about 3 times that what they bill the insurance company.

If you are paying cash they will always lower their bills big time to accomodate you.

This can happen but it's arbitrary. I needed to be hospitalized without insurance and the hospital wouldn't budge on the bill. Likewise I had a roommate who had a $40,000 concussion once and the hospital wouldn't negotiate that bill, either.