Don't dismiss this too quickly, I've come across it before. I'm no authority on the subject,this is what I vaguely remember reading (ATPL human factors). When you are in an oxygen deprived environment, your body adapts as best as it can. When suddenly there is 100% oxygen available in the lungs, all the cells in the body open up to accept this 100%, even when this oxygen hasn't reached them yet. This causes a momentary worsening of the hypoxia symptoms, rapidly followed by recovery.
Those mil guys will not notice this 'phenomenon' if they are flying on 100% oxygen all the time, correct me if I'm wrong.