They keep careful track of which animals are bred with other animals to try to keep as much genetic diversity as possible, while also trying to selectively breed.
Well, being a horse fan myself, I can tell you it's not about diversity, it's about trying to reproduce the exact same genes or nearly the exact ones in the next generation. That's hard as you say you never know what other "bad gene" would pop up if you don't select the other parent right.
Race horses are quite inbred to get to what they are...You don't breed a donkey with a race horse for diversity for example. Sorry eagles, but I don't agree with you.
Edit: I would call it bad breeding, not inbreeding. It has nothing to do with crossing siblings. It has to do with breeding the bad genes and not knowing what you are doing, as we often happen to do in the fish hobby, including myself.