The way you assert it to be, it may very well be in practice, and it may very well have been upheld by the courts. But the courts have upheld a lot of laws for a long time before they were overturned, and no law, military or civil, is special in this regard.
But more than that, the situation with Bradley Manning is also clearly wrong. The requirement to obey lawful orders goes hand-in-hand with the responsibility to only give lawful orders, and that carries all the way up to the top: the commander-in-chief (i.e. the president).
Where does his authority come from? The constitution! He also swears to uphold it, and he literally has no authority to command anyone to disregard it, in whole or in part.
Or else, if the US really is about fetishizing military discipline to such a crazy extent, then fuck it. But I don't think so.