You are more correct, but I think the truth lies somewhere between your statement and theirs. We have correlative evidence that lower calorie diets and/or fasting results in longer lifespans, improved insulin sensitivity, pancreatic cell responsiveness, blood pressure, oxidative-stress measures, and more, in humans. We also have animal testing showing causative evidence that fasting produces longer lifespans. Of course, animals are not humans, and correlation does not imply causation. Still, we do not currently have causative evidence that smoking causes lung cancer, and we widely agree that that is harmful for lungs. With enough correlative evidence I think it becomes reasonable to accept it as actionable evidence.