Expansion of mental healthcare access is definitely exaggerated in terms of how much it will reduce gun violence, but in this case, Holmes did have a history of mental illness that was left untreated for most of his adult life. He should have had easier access to mental healthcare, but the important variable in preventing the shooting is that he should not have had the ability to purchase a gun based on his mental state.
I bet there are many people who pass all psychological tests as I don't think it's too hard to pretend that you are a sane person (if you are not a total madman). There are many shootings happening everywhere and somehow all those insane people get their guns...
Holmes had a
documented history of mental illness. Background checks would've clearly made a difference here.