It isn't so much that calories in/out is false, as the equation of "calories eaten - (activity + bmr) = weight change" that is false. The food you eat has a massive impact on your biochemistry (and thus your metabolic rate), and microbial metabolism also varies significantly depending on the substrate you provide them.
The beginning of the article linked says "if you usually consume 2,500 calories a day and then cut back to 1,600 calories, you’re going to lose weight from that 900-calorie daily deficit — even if all you ate was potato chips. But you won’t be healthy and you most likely won’t be able to keep the pounds off."
I went from 245lbs to 185lbs by eating 1500 a day every day for 5 months, that was over a year ago and I still weigh 185lbs, all I did was when I hit my target weight was make sure that over a week my diet averages out to 2500 a day, some days I go over by a few hundred, the next day I just under eat by a few hundred so that it balances out.
Yep, eating a balanced, calorie reduced diet for a period of time will let you lose weight in a healthy manner - assuming no other issues. Thankfully, most people don't have issues beyond being overweight so loosing weight for most people is just stop eating so much.
Calories in, calories out is indeed how it works, but people also need to realize that your body is not a static machine, it reacts to its environment. Restrict caloric intake too much and you hit a point where your body enters a 'starvation mode,' it holds back on as much work as it can and holds everything it doesn't use. If you have problems absorbing foods due to problems with your GI tract, you might find that you don't need to restrict too much before that happens because you weren't getting all the calories you thought you were before.
Of course, reducing calories will cause your body to change some of what it does even if you have no other issues, so for maximum benefit, you should pair it with exercise.
I've also restricted myself to 1500 calories a day for the past month or so and have lost about 10 lbs so far and am on track to lose a similar amount in a similar time as yourself. My wife did the same thing at the same time, it's not going anywhere near as smooth for her, but she has GI issues.
Citation, please.