Threading the gri gri wrong is not a hard mistake to make, but belaying with it threaded wrong is only possible by being careless. A quick upward jerk on the climber side of the rope tells you all you need to know. I do it every time.
And most climbers who are dropped on a gri gri don't get too badly hurt (unless threaded wrong, which is an inexcusable error). Most errors are the belayer holding the gri gri tight and the climber falling, but at a reduced rate (this is why i always let go of the gri gri when belaying a leader fall, despite what Petzel tells you). Losing the brake hand on an ATC is far more likely to be fatal.
When you say "let go of the gri gri" you don't let go of the brake strand do you? Of course you don't, I just read that weird. Why would Petzl say not to let go of the Gri-Gri while catching a leader fall? I see no reason to touch the device while catching a fall...
Here's a question for all you seasoned (and not-so-seasoned) folks...
How often do you check your regular partners belay set-up before leaving the ground?
I have watched hundreds of experienced climbers make brief eye contact while asking "on belay", without actually checking.
We are human, and make mistakes.
Even with my most trusted safest rad-est partner I do not say "on belay" unless;
1) I inspect his tie-in
2) He inspects my belay set up.
And I'm a 10 year climbing guide (20 year climber).
Every. Time. Period.
I've started tie-ing in incorrectly intentionally to see if my intermediate and advanced clients can catch it before I leave the ground. Like just tie-ing into my leg-loop or not finishing the figure-8 cuz I was busy telling some story... Of course I don't climb if they don't catch it and we can chat about how little things like this can get over-looked after years of climbing. Complacency is a killer.
Oh, my almost grounder on Junco was from an improperly threaded Gri-Gri... I was cleaning it on top-rope... rope feeds smooth since it's a slow progression, unlike clipping during a lead. Neither I or my very trusted partner checked the GriGri... my partner had 2 years experience but never with a GriGri. As I was being lowered all seemed normal until I got on the vertical and started free falling. Luckily she was a strong girl and arrested the fall with brute strength after only 15 feet. I clipped the closest bolt direct while my other partner discovered the issue... f'ing scary that was...
My fault for not checking before leaving the ground.