Maj. Hasan was born and grew up in the US and was quite American. He was scheduled to go to Afghanistan and serve as a psychiatrist--he was never going to see any combat, much less combat against fellow Palestinians.
Hasan having PTSD? The man never served a day in combat, indeed was never deployed anywhere outside of the US unless he went to some kind of international conference. If he had PTSD, it was from some civilian event. IF is the key word, here.
I think a lot of speculation is premature, since autopsies are still being done on the deceased, forensic evidence is being gathered, and Hasan is still in the hospital, but asking questions isn't inappropriate.
Vigilantism is never appropriate. Jumping to conclusions without facts does no one any good.
However, if asking questions now on how this could have happened can prevent another situation from happening, and it's done respectfully, then I don't think that's disrespectful to the dead. Indeed, we owe it to the dead and wounded to find out all the answers we can to prevent a similar disaster in the future.