If I had a nickle for every news report I ever read that said something like "I would never have expected him to carry out such a heinous act"...I would have a lot of nickles.Not a problem at all. Most crazy people who shoot a place up, everyone in their lives knew they were crazy, and a thorough background check would have determined that.
When I applied for my job, or tried to get a mortgage, or sponsored my wife for a green card, I underwent a thorough background check. Had to submit hundreds of pages of documentation.
When I applied for my IL FOID card, I pinky swore I wasn't a crazy person or a criminal.