Mentally unstable people and access to tools for harm

If someone is not mentally stable enough to own a gun, are they mentally stable enough to own a knife, drive a car, own other tools that could cause harm (i.e. even a pencil), or live freely in society?

Women delivering newspapers in Torrance shot in manhunt for ex-cop - latimes.com

Women delivering newspapers in Torrance shot in manhunt for ex-cop - latimes.com: "Chase said that in both instances police came across vehicles they thought were similar to the one Dorner is believed to be driving."

How could that happen? It the emotion running so high that it impairs their judgement?