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My opinion is that it is a "motte-and-bailey" type of a model. Technically correct, but skips some of the important parts.
Things you can control directly:
Things you cannot control directly:
Things this model doesn't even mention:
As a consequense, these things happen in real life that the model does not predict:
If you are lucky, you can actually put a lot of calories in your mouth without getting fat as a result, even if you are not exercising hard. Not sure what exactly happens, my uneducated guess is that the metabolism only takes as much calories as needed, as the rest goes to shit. (So yes, technically it is "calories out", but it is not what people proposing this model typically mean, and you have no direct control over this, i.e. you can't simply decide to lose weight by going to the bathroom more often.)
If you are unlucky, the "calories in" get converted into something that is somehow not easily accessible as an energy source. (Either because your metabolism is fucked up generally, or because your body is low on some important component, such as iron.) You know you should burn some calories, but at the same time you are weak as a fly, so you really can't. (Not because "math doesn't work", but because the linear model ignores some parts of the reality.) But you mentioned this in the "random thoughts" part.
...however, assuming that the metabolism is working more or less correctly, the model is useful.
My recommendation would be:
Step 1 -- get checked by a doctor, whether you are low on something; start taking supplements;
Step 2 -- start exercising regularly, without worrying about the "calories in" yet, just to build the momentum;
Step 3 -- get more strategic about the food you eat.
The reason I put "step 2" before "step 3" is because studing calories can take unlimited amounts of time, and can be used as a convenient excuse to procrastinate on exercising. I would also say that "add a lot of unprocessed vegetables in your food" is a good first approximation for healthy diet.
Other random thoughts:
Agreed. Some people have significantly higher metabolisms.
Agreed. I'm not talking about nutrition, just weight loss.