Cash/Check/Credit/Debit

[classicman]

from Pie's link:

"92 percent of these medical debtors had medical debts over $5,000, or 10 percent of pretax family income," the researchers wrote.

that means their GROSS annual income was $50,000 or LESS. That is not a large number.
Many of them were virtually treating them as ATM's. Many were taking out home equity loans and living off the increase in their home's value. That ride ended rather abruptly. Living beyond their means created the situation, their unfortunate medical expenses just pushed them over the edge.
Also, most of them already had insurance. Therefore, insuring additional people who don't have any currently is not going to change this specific issue.

“The traditional reasons for bankruptcy — illness, divorce and job loss — haven’t gone away,” said Deborah K. Thorne, an assistant professor of sociology at Ohio University whose expertise is in consumer debt and bankruptcy. “With houses no longer A.T.M.’s for paying bills, that escape route is gone.”

It is a three pronged problem.
Illness is a part of it, it always has been, but job loss and divorce rates are at all time highs. They are the real culprits in my opinion, not the health insurance situation. Too many lived for too long on credit and now its time to pay for it - they are. The medical situation is more of an excuse for poor money management than anything else.