I don't know that violent crime per se is a symptom of mental illness. But if a young man walks into a school cafeteria and shoots five people and then himself for no discernible reason, I think that qualifies as a symptom of mental illness. I think the author of this study relies too much on a clinical diagnosis or some prior evidence of serious mental illness. Imagine if a similar study explored the link between hearing voices and mental illness, and concluded that there must be no link because most of the people hearing voices for the first time had no previous clinical diagnoses or any other previous symptoms. The difference is that someone hearing voices for the first time can then go on hearing them for years, while someone who commits gun violence is generally not free to continue committing more. I am also curious why drug and alcohol abuse is not regarded by the author as a form of mental illness.
Are you suggesting that if someone commits a violent crime they must have some kind of mental illness? And that we just haven't defined "prepared to commit an act of violence" as a mental illness.
I'm suggesting that these are commonly held beliefs, not that I hold them personally. More so, I was looking for input on the subject, as my personal experience in this area is virtually nonexistent.