I haven't handled near as many guns as many folks here but I've handled a bunch. I have had 2 guns the "went off" on their own.
1) was a Rem 513 bolt action target rifle that someone had fooled with the trigger. This was in high school rifle club. It would fire just as I fully closed the bolt. Since I was in prone position, muzzle pointing downrange at the back stop, no harm done but it rattled me. Not understanding I tried a second time w the safety on. The trigger seemed to hold when I put the safety on then got fully settled to shoot. As I moved the safety to fire the gun fired - no finger near the trigger. One more try w safety on then off - same thing - bang. I called the coach and we pulled that rifle off the line, removed the bolt and I believe coach took the rifle to a smith. It sure rattled me and even with another properly functioning gun I shot poorly that practice day.
2) air rifle. I partly documented this in the air rifle section on GB years ago. I sent the break barrel rifle to a well known smith but apparently his life was turned upside down with family issues. 2 years later and a bunch of letters, I got the rifle back, supposedly well tuned. I scampered to the basement where I had a small range set up. Fired a couple pellets and the trigger was ultra light. Out of pellets I foolishly cocked the gun (see my error right there) then reached over the rifle for a pellet leaving my left thumb in the breach. It was an awkward reach and a slight jostle released the sear and about 1/4 of my left thumb was nearly guillotined by the barrel and breach snapping down on my thumb chopping a small chunk of bone off too. A 5 hr wait at the ER ( bad timing - a lady was having a heart attack) my thumb was sewed back together. Back home I right away I carefully loaded the gun BEFORE cocking, cocked the gun and the sear released as I began to shoulder the rifle. And then one more time the sear released without touching the trigger. 2 holes in the sheet rock. The sear engagement had been excessively reduced to where it couldn't safely hold the piston mechansim. Luckily I was able to tighten the trigger back up to where the trigger held safely even with considerable test bumping and shaking and I have a safe 3 or 4 pound trigger pull instead of a few ounce pull. I'm not sure what happened to that smith - I emailed him about the problem to warn him. I never heard back.
3) I did fire a gun by mistake when I was small. I could barely cock the hammer on a single shot and in the process of using both thumbs, I got a finger on the trigger. So when the hammer slipped from my thumbs, the other finger was depressing the trigger, the hammer fell and fired the 22 shell. Luckily the rifle was pointed down range safely and I was shook up but learned. All operator error. The gun didn't "just go off" all by itself.
Could be interesting to follow this trial. Such a sad loss of the woman due to multiple people being careless it would appear.