These figures have sometimes been disputed by other scholars, for example this article by Dranove and Millenson in a 2006 symposium in the journal Health Affairs, which argued that the definition of medically related used by Himmelstein et al. was far too broad.
If medical bills are contributing to a higher proportion of bankruptcies in the U.S., we should expect to see this reflected in a higher overall bankruptcy rate than for countries where universal health insurance makes medical bankruptcy impossible. It turns out that this hunch is correct.
In 2006, Rigmar Osterkamp of the Ifo Institute for Economic Research in Munich, Germany, analyzed select OECD countries that had bankruptcy data extending over many years and which clearly distinguished between personal and business bankruptcies. Between 1980 and 2005, the United States opened up a steadily widening margin over #2 Canada, which itself was significantly ahead of the other OECD members studied (Australia, Germany, the Netherlands, Sweden, and the United Kingdom). According to Osterkamp, the U.S. and Canada had the two most debtor-friendly bankruptcy systems, though he noted that Germany's had become much more debtor-friendly in 1999 (leading to a sharp increase in bankruptcy filings), whereas U.S. law had become more restrictive in 2005. He saw this relative debtor-friendliness as the explanation for why Canada and the United States had higher rates of bankruptcy. However, he did not consider what differentiated the two countries.
As we can see from the chart, in 1982 the U.S. and Canada had virtually identical rates of around 1200 per million population, whereas by 2005 the United States was around 6000 per million while Canada was just a little over half that rate. (As Michelle White notes, the 2005 figure was inflated by consumers wanting to file under the more favorable law. According to the American Bankruptcy Institute, the figure plunged to 597,000 in 2006 but by 2010 had again topped 1.5 million filings.)
Without a detailed statistical analysis, I can't prove that the rise in medical bankruptcies accounts for the growing gap between U.S. and other OECD bankruptcy rates. But besides the suggestive fact that the proportion of medical bankruptcies grew in at least the latter part of the 1980-2005 period, we also know that U.S. per capita health care spending opened up a very similarly shaped gap relative to the rest of the OECD over the entire time span. And the finding that the U.S. personal bankruptcy rate is so much higher than that of other rich countries suggests that Himmelstein et al. are more likely closer to the truth in their estimation of the level of medical reasons for bankruptcy than are their critics.