The problem is when people claim that they can lose weight without running a calorie deficit. This is what's obviously wrong, and it is completely fair to invoke thermodynamics as a way to immediately and soundly refute such claims. When someone claims to have anecdotal evidence of losing weight while not running a calorie deficit, the error is not with the "calories in = calories out" equation but with their poor accounting of where the calories are going.
In my experience, people who promote their pet dieting theories (especially ones that promise dramatic weight loss without requiring exercise) using thermodynamically impossible claims are far more prevalent than people who mean lab calorimeter data when they talk about the calorie content of their food. Your comments about gasoline and wood chips are an insulting straw man, because nobody is ever referring to those numbers in a casual context. They're talking about the calorie numbers that can be found on nutrition labels, and those are meant to approximate metabolisable energy, not heat of combustion.