LOL! I have no idea, I don't shoot birds over dogs much. If I had to guess though, it's probably done for training purposes. "Fetch" tells a dog to go get it, but is more of a playful thing (like a ball or frisbee retrieve). "Dead bird" is a working command (it would seem) implying to retrieve it without the hope of eating it, or playing with it. Just a guess though, as my experience with working dogs were either military malinios or working companion dogs for severely disabled people. And in both of those cases, commands were always differentiated between play and work. In fact, once a working command was given the dog was expected to stay in that "working" mindset, until given the "release!" command (accompanied with the handler using the hand motion of two fists together, being pulled apart, across the front of your chest).
But I digress....