I have never done eventing, so this is just a wild guess, but I feel like a good eventing horse would need to be more brave and well-rounded than your average horse shown in one discipline in an arena
So, like...I could see bravery playing a larger part for lower leveled horses (less training/experience) than it would a horse with more training. Of course, I'm just talking shows since I can't really see how bravery would affect a horse's breeding potential.
I've had the same experience with my show horses. I had one mare who would spook at her own eyes blinking and then be perfectly fine with having a gun shot off of her or fireworks going off as long as someone was on her back