What Matt Lalonde seems to be describing is a calorie restricted, low carb diet. Yet as he progressed, he reports muscle development along with fat loss.
The fat loss part is straightforward. I'm curious though as to whether or not the body would create muscle in a calorie deficit. The only explanation I can think of is that with insulin kept at bay, the body had access to high energy reserves through stored fat (so no calorie deficit).
It should be noted that this article is from 2009, back when Mat was experimenting with lower carb paleo... I don't have the link right now, but I believe in a podcast with Robb, Mat described how one day he "hit a wall" and almost passed out from low blood sugar while exercising... I think he currently recommends eating moderate carb (150 g/day) along the lines of PHD.
You should check out http://leangains.com - he doesn't recommend keeping low carb on training days, quite the opposite. But the recommendation is to cycle carbs and calories, and train heavy 3x/week. Have a caloric surplus on training days, a caloric deficit on rest days, which amounts to 3 surplus days and 4 deficit days per week.
But he's got dozens of client testimonials where they lose fat and gain (or at least maintain) muscle/strength.
I don't see anything there suggesting he was calorie restricted. And the whole point of losing bodyfat is that you are burning "enough" calories every day in any case. If everything else you're doing is creating an environment for building muscle, then the necessary calories will be factored in to what your body wants to burn.
The point he's looking at is whether you need to desperately refill muscle glycogen after exercise in order to recover. And the results are that it's inconclusive. My take on that is that it depends on your regular diet. If you eat low carb then when you eat is not really an issue.
Low carb/low kcal diets aren't perfect for building muscles. Neither is a vegan or near vegan diet. It's however possible and if one is far from one's genetic peac regarding muscle tissue, it's not that difficult either.
I had similar experiences on a PSMF diet where my calories were very low, carbs non-existant, and the bulk of my calories were coming from protein.
And I felt like crap.
The gains weren't as fast as they would have been if I had been following a GOMAD protocol, or the "Eat Everything in Sight" protocol, but gains to strength did come... albeit to more "technical" lifts, so my reduced weight could have simply improved my flexibility and ability to do them.