A soldier is supposed to support and defend the Constitution of the United States, as well as obey the lawful orders of the President. If President Obama really is not a natural born citizen, then he would not be the legitimate President, and would be in violation of the Constitution. In that situation, I would argue that the soldier would be doing the right thing; however, as much as I dislike Obama, I think the whole issue is wishful thinking. I do give the officer props for having the courage of his convictions though.
Also, keep in mind that an officer receives authority directly from the President, whereas NCO's receive their authority from Congress. If Obama really is not a valid president, as dictated by the Constitution, then there would be problems.