It is physically impossible to gain weight while eating a caloric deficit. The same kind of impossible as perpetual motion.
Burning fuel in a calorimeter is not the same thing as a human body. /Fat/ loss and creation aren't the body's /only/ response to calorie deficits and excesses. You can create new /fat/ cells while still losing energy and mass overall without violating thermodynamics. As I said above, all you need to do is have your metabolism prefer your other stores first.
Is it? As much as I want to agree, what if my body decides that 50% of calories input must be stored? It might mean that I will have to eat 200% of my daily required input just to be functional.
Not saying that this is the case, but I think it’s what the article is arguing.
Your body requires some number of calories to keep the lights on for a given day--to move, to breath, to run your brain. Google says the average is 1800/day.
If you only eat 1700 calories per day (a 100-calorie deficit) for a month, and you don't stop moving, breathing, or thinking, then your body managed to get those missing 100 calories from somewhere (i.e. from fat).
In your example, say you burn ~1800 calories per day, but you only eat 800 calories (a 1000-calorie deficit)--and your body, because it hates you, stores all 800 calories as fat! Well, your body still used up 1800 calories (assuming you're still breathing, etc). So you would've burned 1800 calories of old fat, and stored 800 calories of new fat. But wait! Turning fat into energy isn't free, that requires energy, too! So you'd actually be burning more than your base rate of 1800, meaning your deficit would be even higher than the expected 1000.
It's all much more complicated than this. Your body has multiple ways of generating energy, storing, and releasing energy. Eating less signals your body that you need to preserve calories, which may lower your metabolism and make it harder to eat a caloric deficit. But at the end of the day, physics dictates that you can't get more energy out of a system than you've put into it.
If you don't eat enough, you'll feel lethargic and unable to perform normally, so I doubt it will still use 1800 calories. According to the article, if you eat 800 calories and your body stores them all, you'll feel as hungry as if you never ate at all.
Of course this likely isn't so drastic ("50%") but it would explain why many people keep gaining weight over their lifetime (or until the body reaches a balance).