I'll just add since my reply was a bit short - that if not for the danger of losing sight of the point here, I could continue your deductive argument with a list of examples which seem to support the rule and could criticize your chosen examples, but the important point is that statements of these kinds are not philosophically known to be false in most given contexts. The naturalistic fallacy is actually a strong case that they are false in philosophy of ethics, and this has been ideologically amplified to teach that they are false in all contexts. Its terrible education, not fallacious at all to say: "my cats natural diet is small mammals, so its probably better if I dont feed it too much bread and mayo." etc.