Crews lift boom from wrecked house
I operate cranes once in a while (I even have an OSHA card for a few of them), there's absolutely no way I'd allow anyone to be in any structure that I'm lifting over.
Too much can go wrong too easily. Like the house in the story.
The crane that tipped could likely lift 100 tons, if it was close to the load. Any cranes capacity goes down quickly with distance. A 100 ton crane will only lift about 10 tons 100 feet out.
The boom on a big crane is incredibly heavy, and usually cannot be retracted unless it's up a bit.
Trees are some of the worst things to lift. There's no way to know what it weighs. Just about anything else is a known weight, and is much safer.