@wildwood
I don't know what it is with woodpigeons: they are one of the most skittish creatures I can think of. They take flight, from positions of complete safety and concealment, in the treetops, when I'm over 50 yards away. And I take care not to walk loudly or disturb the wildlife.
If the bests are that flimsy, maybe the one on the nest took off with such force that they knocked the whole structure down? TTG said he found just the chicks on the ground, not an entire broken nest.
Thanks for the extra info though. My thinking was that, if the odds of a chick falling out, by accident, were small, then the odds of two falls would be vanishingly small. This doesn't allow for the fact that accidents have reasons and a big hole in the right place would make two falls inevitable, rather than improbable.