What is the real source of the medical adverse selection problem?

Ray Fisman reports on the job market paper of Nathaniel Hendren, an MIT student on the job market this year.  Here is an excerpt from Fisman's piece:

…sufferers of heart disease and cancer have greater self-knowledge than healthy people in terms of what their likely medical care costs will be. The market for insurance unravels, in Hendren's model, when patients have a clear view of their future health care costs and people who anticipate lower-cost futures self-select out of insurance coverage.

It's not about knowing more about your state of health, it is about knowing more about how costly your treatment will be.