There is no thermodynamic law stating that fat cells must release fat just because your body needs it. If you're built so that weight loss is impossible and you try eating less, your metabolism slows down - possibly in much the same way it would as if you tried eating less and you had no fat cells whatsoever. I can't cite studies but wouldn't be particularly surprised to see that muscle gets cannibalized instead of fat being lost, if you try to eat less than the most slowed metabolism needs. And if most metabolically disprivileged people stop trying to eat below their minimal metabolic rate before doing significant damage to themselves, that's just the survival instinct kicking in. I would seriously not be surprised to find that fat people have starved to death without their fat cells releasing fat, and blinded by preconceptions, nobody managed to notice or note down when this occurred. But I would expect that to be rare - most people, if their body tells them they're starving to death, will eat. This gets cited as weakness of will.

Metabolically privileged people assume that if you eat less, your fat cells will release fat. (Bitter laughter.) No. We don't have energy storage units like you do, we have energy retention units. Calories go in, they don't come out. Or if they do, it's on special occasions we don't understand how to predict or trigger, and which don't have any obvious relation to attempts to eat less or exercise more. The laws of thermodynamics do not require that a physical fat cell physically release stored lipids when you eat less or exercise more - and if your fat cells are malfunctioning, they just won't.

In that case medical interventions to remove fat directly are inadvisable as the fat will simply be regained, psychological treatment is required instead.

This is simply wrong. If you start out metabolically disprivileged, medical interventions to directly remove fat result in reduced appetite as your fat cells no longer suck glucose and fatty acids out of your bloodstream.