Over an extended period, yes, this bears out because the law of thermodynamics. But the question is - can people adhere to a calorie-restricted diet long enough to see meaningful results? More importantly, will they simultaneously be able to build muscle and maintain normal bodily functions (thyroids tend to stop functioning normally during extended calorie restriction, especially when fat intake is low)?
You will have a much easier time achieving a healthy body composition and feeling satisfied while eating a high fat low carb diet, than you would eating the same amount of calories on a low fat high carb diet.
I say that the "calories in, calories out" approach to dieting is problematic because it's simply not as effective as switching to a HFLC diet. It makes building muscle tissue difficult, it encourages miserable dieting tactics, and taken to the extreme (which many people do) is a threat to a person's health.