The study of medical bankruptcies has been under attack for not taking proper account of the effects of the change in bankruptcy law in 2005. The authors are accused of leaving this out of the article, or at least obscuring its effects, and the suggestion is that this has been intentional. However, reading the study I find that they deal directly with this issue:
Changes in the Law
Between our 2001 and 2007 surveys, Congress enacted the Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA), which instituted an income screen and procedural barriers that made filing more difficult and expensive.
The number of filings spiked in mid-2005 in anticipation of the new law, then plummeted. Since then, filings have increased each quarter. They are likely to exceed one million households in 2008, representing about 2.7 million people.
BAPCPA’s effects appear nonselective. Current filers differ from past ones mainly in having struggled longer with their debts. New restrictions fall equally on medical and nonmedical bankruptcies, with no preferences for medical debts or sick debtors. It is implausible to ascribe the growing predominance of medical causes of bankruptcy to BAPCPA.
Conversely, there is ample evidence that the financial burden of illness is increasing. The number of under-insured increased from 15.6 million in 2003 to 25.2 million in 2007.3 Of low- and middle-income households with credit card balances, 29% use credit card borrowing to pay off medical expenses over time. Collection agencies contacted 37.2 million Americans about medical bills in 2003. Between 2005 and 2007, the proportion of nonelderly adults reporting medical debts or problems paying medical bills rose from 34% to 41%.
You can disagree with their methodology, e.g. I have questions about how causality is measured among other things, but I don't see how you can accuse them of ignoring the issue when they say, plainly, that "It is implausible to ascribe the growing predominance of medical causes of bankruptcy to BAPCPA."
It's also important to take some time to read the references before issuing sweeping indictments of the research, people are expected to read the cited references when they have questions. In footnote 7 above, the issue of how the sample changed due to the law and what difference that might have made is discussed in great detail. For example, here are a few graphs from the paper (and this is just one of the many references they include, note also that Elizabeth Warren is one of the authors of the paper cited in this footnote):
There are additional figures showing how secured and unsecured debt, assets, and other measures relative to bankruptcy changed over the 2001-2007 time period. Here's the conclusion from this paper:
VI. CONCLUSION The Consumer Bankruptcy Project is the first random national sample of families that filed for bankruptcy after the 2005 amendments. Our initial findings should dampen the enthusiasm with which some trumpet BAPCPA’s success in reducing the number of bankruptcies. The principal feature of the amendments was an income-based screen that was supposed to differentiate can-pay debtors from their can’t-pay counterparts. The data suggest that this failed: there is no differentiation based on income, either for the sample as a whole or for the division of families into Chapter 7 and Chapter 13. Instead, the data suggest that the incomes of the families filing for bankruptcy after the amendments are indistinguishable from the incomes of the families filing for bankruptcy before the amendments.
By its own design, the means test focused on income. It did not take account of the overall financial condition of debtors; net worth and debt-to-income ratios were irrelevant to the new law. While secured debt received some favored treatment, the size and impact of unsecured debt loads, such as credit card and medical debt, were largely ignored. With only slight exceptions,  families that owe a little and families that owe a lot of unsecured debt are equally eligible for Chapter 7 relief once they have survived the income-based means test. Yet this is where our additional findings reveal important differences with the 2007 filers. After the amendments, families filing for bankruptcy owe more debt, particularly more unsecured consumer debt, than their counterparts from 2001 and are having a much harder time servicing that debt with disposable income.
The higher debt-to-income ratios among the families that filed bankruptcy in 2007 suggest that Americans are struggling harder than ever before they collapse into bankruptcy. Whether they are discouraged by the negative publicity surrounding the 2005 amendments, concerned about the stigma associated with bankruptcy, or dissuaded by aggressive debt collectors who bully them into believing they can no longer file for bankruptcy, it is clear that families are not turning to bankruptcy even when they have great need. This is a result Congress neither intended nor promised.
They did not ignore the issue of the change in the composition of the sample, and suggestions that they did are dishonest. They are saying clearly that there are no important changes in the composition of the sample that can explain the differences in the proportion of medical filings, i.e. statements such as that "BAPCPA’s effects appear nonselective. ... New restrictions fall equally on medical and nonmedical bankruptcies..."