There's plenty cash-only doctors and clinics out there. There's also companies that handle healthcare for their employees via personal accounts (they put more cash in your account each year, and you spend or don't as you see fit). People on such plans do a lot more shopping around.

And as the other poster said, you always have the right to refuse treatment, up to your death if you like (unless it is some kind of involuntary commitment where you are put there because you are supposedly dangerous). Many terminally ill people choose to go this way.