Arizona is an unrestricted state, meaning no permit is required to carry a handgun. Presumably, anyone who wanted to be armed at that event, could/would have been.
So, permissive gun laws did not prevent/mitigate this shooting, i.e. by resulting in a sheepdog (armed civilian) taking down the gunman.
Early reports say the gunman had an "automatic" weapon. It remains to be seen whether this means a semi-auto pistol (like those used at Virginia Tech, acquired legally), or a fully automatic "assault weapon". Chances are, it will turn out that the gunman used an illegal firearm, either acquired illegally or modified. So, it's unlikely that tighter gun laws would have prevented/mitigated it either.
This is a failure of security (to protect the congresswoman, staff, and the public at the event) and possibly law enforcement (to prevent an illegal firearm from getting into the gunman's hands), though Arizona gun laws being as permissive as they are, it's possible the gunman's firearm will turn out to be completely legal.
