Sadly, the equivocation offered by the Wounded Warrior Project folks concerning suicide and service memebers is somewhat common, in my experience anyway.
After my Guard unit got back from the big Sandbox, we underwent a very brief cursory screening for PTSD and the like.
After answering my questionnaire and speaking briefly with a therapist of some ilk, my Platoon Sergeant informed me the he had been "counseled" that as a gun owner in the civilian world, I was deemed at risk, in addition to answering 'yes' to nightmares and drinking. (I'm a frat boy, I drank before we went downrange)
All that being said, post deployment suicide is a horrible problem in our military and among our veterans, but it's downright dishonest that WWP would try to hide behind it.