Same is true with the President.
Except if you are INDEED a liar, like Obama, then it is you who has committed the fraud
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.
But that commissioned officer did have to supply his/her birth certificate or naturalization papers before receiving that commission. Thus it's reasonable to assume that any commissioned officer is a citizen, or she/he would not be commissioned.
Obama never showed a certified copy of his birth certificate, short or long form, with raised seal,etc to anyone before running for or assuming the office of President.