It's not a sport ~I'd~ care for. Any of that kind of cowboying can only damaging to the horses, mind and body. But then I don't care for bronc riding either.
I know I read Flicka as a kid, but I don't remember it. I'm gonna guess, because it's a 'boy befriends horse' story, that in the movie the sport is not treated sympathetically.
There are a lot of "sports" that do harm all kinds of animals. If you ever saw a steeplechase, look how many of those horses take tumbles. Calf roping is the one that gets me.
From reading that other message board, it looks like the "whistle blower" on this tragedy wanted some publicity for some reason.
I don't have the book to hand (it isn't all THAT good a book - for a good horse story I'd rather read Donn Byrne), but I don't remember a rodeo scene - part of the ambience of the book was the kid's isolation on a remote ranch with his cowboy father, sympathetic but ineffective mother, and an older brother who does everything right. But there was a scene where Flicka's mother (a black mare whose name I don't remember - but a bad actor and outlaw that nobody could tame) rears up in the cattle truck as it goes under the ranch gate and knocks her brains out. The boy is of course horrified by this (and the cowboys naturally don't comprehend that).
I'm sure the rodeo scene is more of the kid's horrified reaction to cruelty and violence.