I believe the NRA blamed violent video games too. Not sure why. Don't blame some inanimate objects, but blame other inanimate objects? It's like denying guns are problem but affirming cars are in need of regulation, or vending machines...
My take:
It's pretty clear that mass murders are caused by mentally challenged or mentally ill people (more often the mentally ill), generally with known track records and even government files describing/warning about their behavior, who then reach for the same privileges of responsible citizens, and fail miserably to handle themselves responsibly. It's a sociological, perhaps biological, phenomenon. Man is the problem.
Armed security is a good check on the above from happening at public locations. Problem is that even trusted security professionals occasionally flip-out and perpetrate a mass murder themselves (it's proven). And quality isn't cheap.
You can try to take society technologically back to cave-men tech by banning everything, except when in government hands, but then you'd still have Judo and scissors.
Overall, there's no perfect solution to the problem of mass murder. Fund research into humane solutions?