The light weight of the .243 round is an issue, especially if it hits a thick elk bone at 500 yards. A heavier round is more likely to break through that bone and penetrate to finish the job. I know that premium bullets will help, but I'd still prefer a heavier round for that distance and animal.
The kid got lucky that the .243 round didn't hit a shoulder bone and fail to penetrate. Think they'd show hours of tracking a wounded elk on the television show? I doubt it.
Anyway, congratulations to the kid, everything (luckily) turned out well. He'll have a heck of a story to tell his friends!