What is a member of the US Armed Forces supposed to do if they believe that a superior officer has given them an illegal order?
A military service member is obligated not to follow that order. He or she should inform the officer that this is an illegal order and let it be known that they will not comply. Customs and courtesies dictate that you should make some statement to the effect of:
With all due respect, sir, I believe that to be an unlawful order, and I respectfully decline to obey it.
Such a statement is meant to give an officer, unknowing of his offense opportunity to clarify or belay the order.
.. Military personnel do have a choice when facing any form of punishment in the military. They can refuse this punishment in lieu of a Military Court Martial. What they are asking for is to be tried in a military court of law for their own crime. What they are effectively doing is getting the chance to get the entire business out in the open where, if they have made the correct choices, they will be acquitted and that officer will likely have a great deal of explaining to do, probably in the form of a Court Martial themselves.