First of all, I said that 39% of releasing veterans report that they're having difficulties.
I'm not familiar with the study that the library submitted, but I can tell you that, according to a study conducted by Veterans Affairs Canada, and which I believe contains absolutely accurate data, approximately 40% report that they are having difficulties.
You're right in saying that the difficulties veterans experience aren't always medical in nature. They may be related to veterans' employment searches or the way they're adjusting to civilian life in general as they seek a new path. Medical difficulties aren't always the biggest problems for them. The issue may simply be a very big life change.