Guns don't "accidentally discharge." He put his finger on the trigger and squeezed, end of story. You don't need much training not to put your finger on the trigger unless you're about to shoot something. You just need to not be stupid. Sorry, but it's really that simple.
As a Deputy Sheriff I agree with Hector. That gun fired when someone's finger pulled the trigger. At the range, my department trains and stresses over and over "MASTERGRIP". That is your trigger finger never goes on the trigger untill you are going to fire. Most modern handguns have safety transfer bars that make it so the firing pin cannot contact the primer unless the trigger is held all the way back. This virtually eliminates the "accidental" discharge.
I also have no problem with any honest law abiding citizen carrying a gun. The "BAD GUYS" don't sit around discussing this. While my experience with wild animals has always been for them to try to get away from human contact, it is somewhat reassuring to be able to defend myself if Yogi decides that I look tastier than grubs and berries. If it makes you more comfortable to think it couldn't happen or probably won't then don't carry but I will.