Which brings me to the moral of both stories. Breast collars can save your life. I've had it happen twice now, where a saddle has rolled on the horse, and I honestly think that if I had not had a breast collar on both of those horses, the saddle would have rolled under their belly and me with it!
I've seen way to many saddles slip off due to lack of breast collar. One time I had a really heavy guy slide off into a cactus! That was a nightmare of a ride. We were pulling the spines out of him for hours! When you have a string of dudes 10 horses long it's difficult to keep a close eye on each one.
Though a good rider should be able to tell when the saddle is slipping in any way, shape or form, I don't ride without one. Much better to be safe than sorry!