As I get to know these birds more, the less I feel that we "train" them. That hawk was bound to learn to hunt or die trying. The only difference between her and her siblings from the same nest is that if she fails, someone takes her home and feeds her. If her handler does it right, she will have opportunity after opportunity to learn to hunt all kinds of game. A wild bird often gets less training and a much higher chance of getting whacked in the bargain.
Wild redtails will often develop prey preferences based on their past successes. Released or "gone wild" falconry birds are often generalists that have learned to take anything and everything.