As Schlud said, it is a matter of conditions. Here in Florida ATs are great as long as you don't play in the mud. Unfortunately, if you off-road in Florida, you play in either sand or mud, period. I have been surprised at my ATs ability to get through the mud, but they definitely aren't mud tires.
As for breaking beads, I can tell you it can happen to anyone. Aired up, aired down, it is a possibility. The mudhole the two Long Trails blew in was a mud hole I had just driven through myself along with three other trucks with no problems. It was just luck of the draw. They hit it the same way and both got lucky. It just proves that rocks aren't the only place you can pop a bead.