The Washington Post piece I linked to (Permanent URL: <http://web.archive.org/web/20180326154159/https://www.washin...> discusses the Himmelstein article the letter you cited cites. As arpinum said, Himmelstein et al. conflate any debt that includes medical bills at time of bankruptcy with "medical bills caused bankruptcy".
Neither of your links are primary source data and give an incorrect interpretation. If you follow the links to the primary data you will find the phrasing changes from "medical problems contributed to..." in the source to "health care expenses were the most common cause of bankruptcy" in your citation.
The numbers you cite are the percent of bankruptcies that include medical debt. The data doesn't say the medical debt caused the bankruptcy, or that this debt type was the largest percentage of debt. People declaring bankruptcy typically have many types of debt as they generally fall behind on all their bills.