Well one thing that article doesn't mention is that the scale isn't your ultimate guideline for how much fat you've lost or how much muscle you've gained. Gaining muscle is extremely difficult unless you are a 19 year old male pumping full of testosterone and are beginning a heavy weight lifting regimen. That doesn't mean we can't gain muscle, I just would never describe it as an easy process.
There is also the fact that your muscles retain water as part of their healing process. So it isn't unusual for someone to lose inches and the scale stay the same or even go up if they are working out.
And of course when people say muscle weighs more than fat, I usually think they are talking about volume because if you had 2 jars, filled one with muscle and one with fat, the one with muscle would weigh more.
You can't out-exercise poor eating habits.