Nowhere did I say that the calories out have to be as a result of using them as fuel, calories can be used as sweat, food for mosquitos, excrement, anything you'd like. The fact is that calories in < calories out = weight loss. Show me any example where that wasn't true and you'll demonstrate how to violate the laws of physics. That's just how things work...
If you want to be pedantic, yes that's correct, but in terms of weight loss and actionable advice it's beyond fucking useless.
The reason being is that all 3 of those items are at best within your control directly to a minority degree, and depending on the circumstance, the resultant one with be a function of the other two, while simultaneously all working in concert.
Calories in is governed by hunger, which is governed by activity levels, body temp, types of food eaten, and a host of other aspects. Sure you can just "not eat", but you're fighting 2 million years of survivalist evolution, and not a viable long term strategy. Are you saying everyone at a healthy weight has been famished their entire life? How do you reduce calories in, while maintaining calories out?
Calories out is determined by activity levels, but also how much and the type of food you've recently eaten, temperature, stress, how rested you are, and a host of other factors. If the body has less calories than it wants, then you can become slow, lethargic, body temp drop a bit, basically all sorts of things to reduce your calorie burn. You could say just keep exercising, but it's like being up for 3 days straight. Eventually the body says no more energy to run as it says no more wakey time. How can you ensure calories out exceeds calories in without energy levels/BMR/Body temp/wakefulness crashing?
Weight loss is determined by energy balance as you insinuated, but also hormonal changes. Why do bears about to hibernate and pregnant women put on fat? Why, even if they eat the exact same calories as before, do they *still* put on fat, while at the same time the above energy conserving tricks kick in? It's because the body has made fat retention a priority. Aside from what I've mentioned, what causes the body to prioritize fat creation/retention?
I also highly recommend the book "Good Calories, Bad Calories". It's filled with interesting studies, but is a bit on the technical side. Studies where calories in people with stable weights were replaced with fat, protein or carbs, and if all calories were equal, you'd expect no change in weight, but that wasn't the case.
Studies where people were not hungry on a sub-sustenance protein/fat diet, but add in 500 kcals *extra* of carbs, and then they are starving.
The above "fat first" body prioritizing gets some mention, and all in all it's a great book. He compared the body to a 6 sided teeter-totter. If you change one thing such as fewer calories, than a host of other things will try and compensate to ensure nothing in the body changes. (massive hunger, lower BMR, more tired, etc.)
I find the whole topic fascinating. You have very highly educated people on both sides, hundreds of studies many of which show conflicting results.