The rock was not "teetering". It had been sitting in one place for as long as anyone can guess. No one can say how much longer it would have stayed in place.
There are lots of these formations all over the world, some are much larger. If they bother you, stay away from them. The whole reason we have a park service is because some people just can't resist defacing and destroying everything in their path.
That these guys were scout leaders tells you all you need to know about the level the BSA has sunk to.
Honestly, take a deep breath and relax. Your analogy to Mount Rushmore is totally off base.
What these guys did was on the stupid/careless side. But I’ve seen a lot worse stupidity. Was this formation somehow marked as special or keep off? My guess is no. Given this, I think the public flogging their getting is overkill. Pressing charges is beyond the pale.
In the end, I think their biggest “crime” is looking like a bunch of ignorant buffoons.