Strange paper. I appreciate the attempt to view fat gain as a consequence of metabolic disregulation, and like the analogy of the little tank/big tank.
The overall model posits that the body is much more sensitive to changes in glycogen than in fat, and that changes in glycogen drive overall food intake. Generally this, mechanism works to keep weight stable over time, but a metabolic mistake that drives fat accumulation may run for a long time before self-correcting, because the body is much less sensitive to changes in fat than to glycogen storage. The paper posits a mechanism whereby the modern diet keeps glycogen storage constantly full due to high availability of high carbohydrate foods, driving fat storage from the high fat content of the western diet. (The phenomenon of insulin resistance is mentioned in passing as an alternative driverof fat accumulation, but the overall model explains why both might happen without self-correction).
That model would explain glycogen depletion favors fat mobilization and oxidation, and would explain how both a high fat low carbohydrate diet would favor fat loss (so long as the carbohydrate intake was low enough to prevent full glycogen replenishment).
It would also give a model for explaining why HIIT promotes greater fat loss than steady state aerobics (again, through glycogen depletion).
The strange part of paper is the dismissal out of hand of a clear pathway from high carbohydrate ingestion to lipogenesis (based on one paper). There's a theoretical argument in favor of low fat diets for weight loss/weight maintenance, but no reflection of the real-world fact that low fat diets tend to do worse than low carb diets in clinical trials.
Then there some just silly stuff about how weight lifting tends to promote weight gain and long distance aerobic exercise tends to promote weight loss, based on a theoretical model calculated from the ratio of food quotient to respiratory quotient, leading the author to conclude that short duration work is counterproductive to weight loss (at this point the author, who previously was careful to talk about body composition and adipose accumulation/loss, now talks more vaguely and much less usefully about weight gain/loss).
The overall sense is of an author who is on firm footing when discussion empirical findings in metabolic studies on mice, but falls substantially when trying to apply those findings to the real world...