Don’t know about this mass shooter, but most can pass the background check. Adam Lanza could legally buy a rifle, but not a handgun due to his age. The Columbine shooters were to young and used a straw buyer instead.
Your common criminal never goes thru a background check, even if he could pass it. He doesn’t want a gun tied to him.
Point; Background checks will never stop most shooters.
Adam Lanza would have been refused if his Psychiatrist was worth a damn. They have mental health requirements also on the form.