However, as the GP claimed the “gasoline is a strawman”, and “that’s not what people refer to when counting calories”; these two cannot live together with a thermodynamic argument in any useful sense, because it amounts to “well, if your food labels say a number higher than your exercise machine and BMR, the your numbers are wrong for reasons I cannot point to”, that’s about as helpful as a religious argument.
You can lose weight easily without caloric deficit in any sense - water weight (limited amount of course). There are several other ways in which the body loses fat - e.g. through the skin and scalp (negligible amount for most people, but not all people).
Invoking thermodynamics as an end-all be—all argument is dishonest even if it is a useful approximation.
Water weight is similarly important and still conserved in terms of energy. It might seem meaningless to you, but an athlete who wants to stay at absolute peak performance may want a more accurate picture of what’s going on.
No, it really doesn't. Just look at the sibling comment that claims once again that it's possible to lose weight without a calorie deficit. That statement is wrong no matter how good or bad an approximation you have of what fraction of the heat of combustion is metabolisable.
If someone believes that they are losing weight while eating a diet whose nutrition labels indicate a much higher calorie count than their estimated calorie expenditures, then it's obviously wrong for them to claim that they are not running a calorie deficit. Instead, the reasonable and scientifically valid claim they could make would be that they are metabolising a much smaller portion of that diet than a normal person would, and thus they are running a calorie deficit because lots of calories pass through them unabsorbed.