In general soldiers do not need to *be* citizens. Although joining the military is a shortcut to citizenship. (You do have to be a *legal* alien however). Officers though, must be citizens. Naturalized is fine.
For example, the Air Force Colonel who headed up the Clementine mission which first found water ice on the moon, (They were testing sensors developed for Strategic Defense.) is a naturalized citizen, his family having fled Castro's Cuba when he was a pre-teen.
Officer candidates must indeed prove their citizenship before they are commissioned. Enlisted must prove they are a citizen *or* a legal resident alien.
BHO,OTOH, needs to prove that not only is he a citizen, but that he is a natural born citizen.
Thanks for educating me....I had a little bit of doubt in my mind when I posted that....