It's a common story when people start to eat 20% less, continue the same lifestyle and lose exactly zero weight as the result. Their body didn't create 20% of energy out of nothing but it just started to waste less energy as body heat.
Anything that can influence "energy out" is by your own definition "relevant".
The body is more like a thermostat system. Environmental effects can convince your body to move the temperature/weight up or down, but for both weight gain and weight loss is a battle. Your body tries to maintain it's understood ideal weight. Your body if given a chance and you haven't convinced it to change the thermostat setting, will immediately do all it can to gain/loose weight. This is why crash diets never work. It takes sustained effort to convince your body that it's wrong about your initial weight.
These are excuses, in the fitness community, the response to "I can't lose weight" is "eat fewer calories", and its incredibly effective
When caloric intake is reduced, the body can decrease this type of expenditure without the person even realizing it.