All WW1, WW2, and Viet vets were told exactly this and it worked for most.
Well, in the RAF during WWII pilots who suffered from what we now know to be PTSD were classified as LMF, Lacking Moral Fibre. It was not a particularly rare occurrence either.
Soldiers who fought in the first and second world war were often haunted by their experiences. I'm sure many would have benefited from some sort of counselling. Don't know if I'd be so quick to throw around Vietnam vets in that context either. I personally know several who are still seeing counsellors today.
Some people just don't deal with massive amounts of stress as well as other people. This does not make them weak minded or lacking character or of being cowards.