Okay then, so WHY were they at a shooting range? Didn't Kyle tell his wife that a woman approached him in a store parking lot and asked him if he could help her son who is suffering from PTSD (Routh)? Perhaps this woman was not really Routh's mom and Kyle was being set up? If Routh didn't really have PTSD then what is the basis for the three going to the range? The story falls apart if Routh doesn't have PTSD. That is critical for Kyle being in his presence, isn't it?
Routh being a Muslim convert isn't enough for explaining why Kyle was 'helping' him at a firing range. Perhaps Routh was an operative for those wanting Kyle dead and the only way they could get Routh with Kyle AND ARMED was to use a PTSD LIE to get them together at a firing range..