I am also a military member and you seem to be misinformed about the UCMJ. A military member is only required to follow a LAWFUL order. Your analogy of ordering a private to do something is erroneous. If you ordered a private to shoot your general and he refuses, then he WILL NOT be charged with insubordination. Likewise, if an Iraqi dresses in a stolen US Cpt uniform and orders the private to do something that the private believes is unlawful, then he WILL NOT be charged with insubordination if he can prove either the order was unlawful or the person giving the order did not have authority to do so. This is exactly what many people are questioning and it is lawful.
I suppose it made too much sense.
If you order the private to report for duty and he refuses, then he will be. The military takes a dim view of members who decide for themselves what orders are lawful and what are not. Don't believe me? Google Micheal New or Ehren Watada and see what happens.
Not exactly true. The manual for courts martial says a an order is to be presumed to be lawful. http://www.au.af.mil/au/awc/awcgate/law/mcm.pdf
(a) Lawfulness of the order. (i) Inference of lawfulness. An order requiring the performance of a military duty or act may be inferred to be lawful and it is disobeyed at the peril of the subordinate
A lawful order is also one that is related to the normal conduct of military operations, and while the issue authority is important it is not the final word, because:
Authorization may be based on law, regulation, or custom of the service.
At risk here is:
However, the dictates of a person’s conscience, religion, or personal philosophy cannot justify or excuse the disobedience of an otherwise lawful order.