I said "no calorie counting", not "eat as much as you please". And by "right proportions" in those books they mean something specific: roughly 50% fat, 25% proteins, 25% carbs, plus a balanced mix of different fats, slow carbs, etc.
The laws of thermodynamics obviously hold for nutrition as for any other phenomena. In order to lose wait you have to eat less, no question about that. But the idea is that it's much easier to directly control what you eat than how much you eat. And by following those diets it's allegedly easier to eat the right amount.
I absolutely believe your method works. As for me, I've experienced that since I changed my diet as per the above recommendations, I'm not hungry two hours after each meal anymore.
tayo42 asked for something less tedious than counting calories, so I suggested they take a look at an alternative approach which has benefited me, and in my opinion is well argued.