Bankruptcy lawyer . . . er, "Toxicroach" argues in my comments section that if anything, medical bills are likely to be overrepresented in bankruptcy filings, relative to the actual damage they do:
People going bankrupt don't pay their medical bills because it's for services already provided. That ranks right below everything else on the priority list. Now, income lost due to illness is a common cause of bankruptcy, but health insurance or not doesn't really change that.