Most of the "hunt"scenes on TV are staged before and after the actual shot. Some will show an impact shot and you will notice that it is almost always darker and grainier than the staged shots. Light is the big issue, most shots are very early or late in the day when the light is minimal. You will notice that, quite often, the animal is shown in the dark. To show quality footage, most of the show will be staged. Most shows are just commercials hawking Camouflage clothing.
And, for the love of God, will someone tell me why they whisper after taking the shot and the effing animal is down!?!?!? Drives me effing crazy...