Seems extremely speculative to me... as PTSD is not responsible for people putting on weight. Medication can have such side effects, depression will often do it... but PTSD??? Think not!
There are plenty of people with PTSD who exercise, are slim, just don't eat and those who are naturally thin, as well as those who suffer depressive effects by eating, along with those who eat because they're bored.
Extremely speculative and unscientific.