Well, hold on.
"In a new report released Wednesday, the bureau shed light on behaviors of shooters before they acted out, finding most obtained a gun legally and did not have diagnosed mental health issues, points that run contrary to some popular beliefs. . . The FBI could only verify that 25 percent of the gunmen examined in the study had any type of mental illness diagnoses, including disorders affecting mood, anxiety and personality. "
Diagnosed. Quite often, if someone has a mental disorder that flares up and leads to a crime (usually psychosis related to schizophrenia or something similar), that is the first time it manifests. They don't have a history of diagnoses. They just break with reality and bad things happen.
It should also be noted that if we talk about "mental illness" generally, the mentally ill are more likely to be the victims of violence in general than its perpetrators. If we're going to look at restrictions on mentally ill people owning guns, we need to make sure that specific kinds of mental illness have at least a very high correlation with specific types of violence.
I'd be interested in reading the actual report, when I have the time. It sounds like it's rather flawed from the start if it counts a lack of prior diagnosis as not having mental illness.