Conflict & Insubordination in the Military?

I'm currious as to how far one can go in a chain of command with conflict and insubordination? I've heard stories where a friend who speaks arabic was always sent on point in Iraq because he spoke the langauge till one day he got sick of it and told the sgt. to go F*** himself to which the sgt simply ordered someone else on point. By brother being mindful of the historic fact that the North Koreans had killed captured medics told his Lt. No when ordered to put his name on his medics aid bag which he intended to loose if the balloon had gone up when he was serving on the DMZ and if it looked like he was going to be overrun and captured. (He had his aid bag specially modified by athe cobbler to clip to the outside of his assault pack and his plan was to simply clip it to the pack of a convient casulty. He had already sanitized anything else on his person that would identify him as a medic).