If I may submit two personal stories in place of rigorous data:
my incredibly poor sister recently injured herself and was facing nominal charges of about $40,000. She was able to get that written down to a few grand and then get donations from family, friends, and charities to cover her bills. She didn't have to "play hardball"; she just explained her situation and the hospital bent over backwards to help her. The hospital staff treated it as a routine occurrence.
My wife and I do not have health insurance at all. We use something called "Christian Healthcare Ministries" [0] which is not insurance, and (at our level of participation) doesn't cover routine visits or small problems, but covers us in case of conditions that might otherwise bankrupt us. So while I personally cannot get insurance on the open market, and routinely get counted in the "not insured" category, I still have coverage.
(Note that I'm not defending the US health care system overall, just introducing some information about alternatives that help people avoid bankruptcy.)