For regular denizens of social media, it makes eminent sense to file a trip plan on FB. I use it occasionally, but you'd definitely miss the regular users if they failed to post immediately on return, if not sooner. It was quick thinking and a job well done. Having carried several injured people out- one girl that broke her ankle on a trail in the Sierra, another that had fractured a leg, falling on an ice patch on the AT in Pennsylvania, I won't rush to judgement that the father was doing something foolish. Accidents happen in the outdoors, not always caused by foolish behavior. I've slipped on lots of loose rocks and scree. Some of the loose gravel over rock that's common on trails in the Grand Canyon could send you to your death quite quickly. My wife slipped on one and had the presence of mind to sit down and not try to windmill or run it out. I'm very glad to hear of a good ending for that family.
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Charlie