That's an interesting thought. I think often murderers like these (and arsonists as well) try to become involved in the investigation somehow. I read a book by the original FBI Profile guy and he touched on this suject. He said it has happened that the murderers often like to help in searches for the body or show up at the scene and act like an innocent bystander (some have even phoned in tips to police)- kind of like the way arsonists like to watch their fires.
If the sniper has a unique way of hiding his weapon, it could be just like you say- he could be at or near the scene when police arrive and just elude detection by blending in with the bystanders.