Sorry yes you're correct, I meant they are not saying that in the colloquial way it is used, which is that it doesn't matter what you eat assuming all else is c

Sorry yes you're correct, I meant they are not saying that in the colloquial way it is used, which is that it doesn't matter what you eat assuming all else is constant (activity level etc). They are saying it in the technical sense that the people did in fact burn more calories on different diets. But those calories being burned were caused by the change in diet (assuming the hypothesis is correct). That is a massive change in American nutrition theory.