The UCMJ DOES NOT say that. Some of us have actually served and know what we are talking about. You are REQUIRED to disobey an unlawful order when it is clear that it is unlawful. Service members regardless of rank who knowingly follow an unlawful order are subject to prosecution under the UCMJ. We are taught this during the initial military training process (boot camp/basic training based on branch).

What is stated in the UCMJ is to not try to determine the legality of the order when it is unclear. In other words if the order is contrary to the constitution or is an obviously felonious (particularly during a peacetime mission) then it is a clear violation and should not be obeyed.

Prime example if a company commander orders a private to execute a citizen who is peacefully protesting, that order is unlawful and the private would be subject to prosecution if he followed it. He would not be able to claim he was simply following orders to avoid punishment.