Cutting calories is the only way to lose weight. Cutting carbs typically means people end up eating less calories, because protein is more satiating.
"Eating the same diet, just a lot less carbs"
If you're eating less carbs, that's 4 calories less for every grab of carbs you've cut out. If previously you were eating around 200g of carbs everyday (probably on the low end, honestly) you've now removed around 800 calories from your diet.
I hope you aren't suggesting that the only ways to lose weight are by lowering intake of calories below your daily usage, or increasing your daily usage of them above your daily intake through some form of additional calorie burning activity...
(cause you'll never sell a best-selling book like that)
I think only the kookiest diets ignore this basic principle. The problem is that most people can't just rationally decide "oh I'll just eat less" or "I'll just eat lower-calorie foods" or "I'll just exercise a lot more and ignore the hunger that comes with it". Well, you can decide that for a variable-length but generally short amount of time, and then billions of years of evolution kick in and hormones make you want to eat more, and eat all kinds of stuff your rational mind tells you is probably a bad idea, but maybe just this once.
Dieting is about tricking that system in one of various ways. Different things work for different people. For some people, no tricks are required but you can't just assume it's that easy for everyone.
The number of calories you burn isn't just a minor detail you can brush away.
Some sources of energy turn preferentially into fat, others promote a higher burning base metabolism. And when you say weight, you're ignoring other factors like muscle mass, water retention, others, that aren't really what we mean when we say lose weight. (Although incidentally, cutting carbs decreases water retention which is one very valid counter to the low-carb weight loss claims.)
Ignoring the very direct counter-statement by OP that he increased his caloric intake and still found success cannot be dismissed.
There are other ways to lose weight. Such as swallowing tape worms, taking a laxative with every meal, using meth, moving to the moon... The statement "Cutting calories is the only way to lose weight" is a gross oversimplification and provably false.
It isn't that simple and a group of us has proved that isn't necessarily true.
Three times I have lead several people through the Whole30 Challenge laid out the Whole9 website mentioned above. We all ate a ton of food and lost fat and almost all of us lost weight. If anything, our caloric intake stayed the same or went up.
(BTW: the goal wasn't to lose weight. It was to become healthier. Last month, someone improved their cholesterol numbers by 93 points by eating that way.)
Assume there are 3,500 calories in 1 pound of body fat.
Then cut, say, 300 calories daily out of your diet for, say, 3 years.
That's 109,500 calories a year or 328,500 calories over 3 years.
328,500 calories divided by 3,500 calories/pound is 93 pounds.
The math isn't that straight forward, but many people use the very math to explain weight loss, at least in the short term. I just can't buy into the math that 'calories in' equals 'calories out'.
That said, I've done the 30-day challenge three times, not restricted my caloric intake, and still lost weight (lost fat quicker than I gained muscle mass). So, even in the short-term, you can lose weight without restricting calories.
* Cutting carbs typically means people end up eating less calories*
Mostly true, but ore specifically, cutting carbs means that you are sending less sugar into your body. Less sugar means it is more difficult for the body to produce fat. Fat is more dense than muscle and the reason most people diet is to lose the fat.
I am not sure this is scientifically accurate, but this is how I make sense of it:
When I eat Paleo, my body thinks it is surround by high quality energy sources. It gets fed those energy sources frequently. The body recognizes that there is low risk that it will go a short period of time without high quality energy. It determines that it has little use for the fat it has stored on the body. The body then converts the fat into energy. Your body enters into a phase where you go for weeks (or months) of high energy because of all the fat you are burning by eating a lot of high quality food---food a caveman would eat.
I mentioned I kept track of all the food I ate in June 2012, and even after increasing my calories after going on low-carb, I still lost weight. What part of that did you not understand?
"Eating the same diet, just a lot less carbs"
If you're eating less carbs, that's 4 calories less for every grab of carbs you've cut out. If previously you were eating around 200g of carbs everyday (probably on the low end, honestly) you've now removed around 800 calories from your diet.
You're still cutting calories.