I have the same issues as Miller with hammer doubles. Grew up with a hammer single, no problems (other than getting the hammer back with gloves on, and decocking if I didn't shoot). I suppose if I'd ever owned a 28ga hammergun or something like that, then maybe I could cock both hammers at once. Otherwise . . . nope, not with my hand.
I do a fair amount of grouse and woodcock hunting, and have taken any number of tumbles. (One of which resulted in a broken rib.) But I've never had a hammerless jar off safe and discharge as a result of a fall. I have had a couple that have fired on closing--guns I just bought, both on a skeet range. Helluva surprise, and really reinforces keeping the gun pointed in a safe direction. And likewise have had some double when the first shot jarred the second hammer out of the sear notch. So stuff can happen, but I've never had it happen due to a fall.