Let's say Ricky Hatton was cutting from 180 lbs. to 140 lbs. over a short period of time. With that rapid weight loss, you're also losing muscle and therefore power. I doubt when he was packing on the pounds he was also hitting the gym to compensate. It just doesn't make sense to me. Even if you lose 25 lbs. at a rate of 2 lbs. a week, you're not going to be as strong.
You can gain muscle while losing fat, and power has more to do with your internal mechanics than it does with the actual size of your muscle.
Gaining muscle while losing fat is not happening if you're an experienced athlete and not using steroids. I agree, mechanics contribute to power, with the majority of your punching power coming from your legs and torque generated by your hips. With this being said, it still doesn't explain how Hatton was able to do it.
You don't need an excessive amount of calories to build muscle. As long as you're getting adequate nutrition and protein during strength & endurance training while burning fat with cardio, it's absolutely possible. Otherwise, every boxer naturally developing their muscles during boxing workouts while trying to cut weight would come in either soft or weak.
Of course you can gain muscle whilst losing fat. Fat is stored fuel and is used as such, muscle has a functional purpose and can be stimulated to encourage growth. They are completely different tissues. Its a science and hence why an expert like Kerry Kayes was brought on board.
The guy was losing fat. He stepped in the ring at 155. He walked around basically obese at 180+. He was just losing fat to about 155 and then just cutting down to 140.