I think this is far more true when you are smaller, like this person, than when you are in the higher numbers. If you're increasing your exercise significantly and building muscle, you are still likely to lose more fat than you gain muscle. A pound of muscle weighs the same amount as a pound of fat, it just takes up less space.
So let's look at it like this. You start off weighing 250 pounds. If you live a sedentary life, a general calorie calculator says that it will take 2338 calories per day to maintain that. To lose one pound a week at a sedentary life, you would eat about 1800 calories per day. You would lose 4 pounds a month. According to
this article, it takes about a month for a beginner to gain a pound of muscle. So if you're dieting and exercising and trying to build muscle, you still should be showing a loss of 3 pounds a month even if you gain a pound of muscle.
If you weigh 160 pounds, you can still have the same thing happen where you are losing more than you gain in muscle, but it's also more likely that you're gaining muscle slightly faster if you've been working on it the whole time AND you're losing slower. So if you're losing 2 pounds a month instead of 4 and gaining 2 pounds of muscle a month, then yes. But when you weigh more, this is far less likely.
I'm not saying you shouldn't find solace in losing inches, because you totally should. And the scale is not the end all and be all. But I know that when I didn't know much about nutrition and was still eating like garbage but working out, that whole muscle weighs more than fat thing didn't really help me out. I was not gaining muscle at a rate which would cancel fat loss.