No. It's not. I've done it and I do it. Maybe if you're close to your maximum potential this is the case. But you made a blanket statement which is false.
Very true! For an example take insanity. Those people didn't have that muscle mass when they started. They also had a much lower BF% at the end.
Let me restate it then. It's impossible for someone who has been lifting for a while and is trying to cut the last few % of their BF not to lose muscle while cutting.
For example, professional body builders as they are building in the offseason eat lots of healthy fats and load up on as much carbs, healthy fats, and protein as they can. When they cut fat to prepare for competition, it's a given that they will lose a sizable amount of muscle.
Obviously a person like the people on the Biggest Loser who haven't done a physical activity in their lives, yes they will gain some muscle. Anyone who hasn't been on a physical training program will gain muscle after starting to work out. So you're right, my blanket statement was not correct. I was speaking more along the lines of people who have been lifting for a while.