Wow, hate to see this happen!
It's hard to tell from the pictures what the case was made out of. I have two guitar cases: one looks a bit like his, but has a "sewn" outer covering sort of a thick cardboard. Would never check this one.
In London, I have a much sturdier case: I can imagine that it has some kind of wood on the inside.
Anyway, not excusing UA or the baggage handlers. If it was checked at the last minute, may have been handled more roughly than necessary - who knows!
I hope that he can make the repair to the tuning pegs, but really, UA should buy him a new guitar!