The problem isn't guns, it's people. Don't get me wrong, I believe in common sense gun laws, background checks and I don't think you should be able to just go into a store and walk right out with a gun, unless you are already in the system. But even if we banned all the guns in the world, people will still kill people with whatever they can get a hold of.
The role guns play is in the death toll, and in some situations, perhaps the thought of causing many deaths is the final nudge that pushes a particular shooter to go on a shooting spree. I think you are right that people are the root problem, but I think guns play an obviously big role here. I do think the infatuation with assault weapon bans is a bit misguided though. It's not going to stop mass shootings. You don't need an AR-15 to murder dozens of people, and previous school shootings
(Columbine, VA Tech) have proven that.
Extensive background checks that take into account mental conditions, FBI tips, social media checks, and ending the gunshow loophole would help a lot. Smart guns that require a person's fingerprints/dna to be encoded as an access lock for the gun would also help, although that technology needs to be developed and refined.