If there is a background check, it can be circumvented very easy. Get your gun on the black market or steal it. The background check assumes, the killer acts lawful at this step of his future killing spree and buys his gun(s) the normal (legal) way. Once they are aware how to go around the checks, they will do it.  Another thought: I remember a video of a black man from Chicago, who claimed, the guns just appear in the troubled quarters, suddenly there are boxes full of gun on stairwells, just for everybody to take. This leads to the thought, IF there are DS organizations involved, they will start to supply the guns. All this blows a hole in your final thought.