I don't think it's the shooting ability itself that leads people to think ex-military, it's the almost invisible nature this person seems to have when looking for a victim. Not that it's really out of reach of the everyday civilian, but the public immediately brings to mind military training when something like this happens in such a stealth fashion.
When we did marksmanship training in the Marines, we started 200 meters from the target and progressed back to 500 w/out scopes. That was everyone. I don't know exactly what a true sniper's range is, but I'm sure it makes 200 yards look like a frisbee toss.
