It doesn't seem like they control for gender either, which is a huge influencing factor. For example, this could be more about attraction than satiation. As in, if you have a fit (more attractive than a fat) waiter, you may not order dessert because you don't want to seem like a pig in front of the hottie waiter. Instead of saying that fat waiters = signal to indulge indulgence, it could instead be that fit/attractive waiters = reminds people not to eat like pigs, and these are 2 entirely different moderators/mediators/variables. The biggest issue is that they have no control so they can't assume any causal explanations. They can only speculate the "why" of their correlations, but even their "why" explanation is very weak and not supported by any evidence from their studies, especially since all they did were restaurant observations without any followups or surveys.