Lifting (power sports) and endurance sports (what I would classify dogs as being involved with. ) are fundamentally pretty different in terms of the stress the put on a body. The goal of weight lifting is generally to stress the muscle to an extreme (to the point of tearing them), they then rebuild bigger and stronger. You certainly need that rest to let them rebuild.
In an endurance sport, you are generally stressing them to exhaustion. You are training them to manage a stress for a long period of time, which doesn't mean they need to be bigger, or even stronger. It's actually better to stress them daily to adjust to the exhaustion. Actually I've done extreme endurance sports, including multi-day stage races (36 hour race weeks) and 8-10 hours races and your body generally does not stop, if trained. What stops most people is improper fueling. I actually loose muscle mass as I get in better endurance shape.