As a shower, and show parent, I can tell you I've NEVER seen live animals thrown away. Chickens are especially easy to over heat and will stress and pass away at shows. Rabbits aren't as bad. Our family has been showing livestock for 40 years. Never have I seen anyone throw away a live animal.
I have however had PETA people throw red paint on my champion rabbits. Their the only people I've ever seen damage an animal.
Generally speaking (there's always one odd out) people who show animals take very good care and have high pride in their animals and that generally doesn't require a "governing body" like a humane society to over see it.