See my Post 26.
"Showing ID can help stop "bait and switch" schemes where a ticket is bought under the name of "Paul Smith" and a very Arab-looking Abdul al-Bombzawi waltzes aboard the aircraft without anybody even asking him his name."
Like it or not, we are at war and the war front has been brought to America's airports with extremely deadly results that have costs thousands of American lives.
During war or even during Peace, ID's are a necessary fact of life in sensitive areas prone to enemy sabotage or attack. On the morning of my last day of duty aboard my last warship, I entered the restricted areas on my own with my ID but I had to leave that afternoon with a Master-at-Arms escort after turning in my ship's ID card.
"Cest la Guerre."
There are many sensitive areas at the moment. Random searches of little old ladies and asking everyone including terrorist sleepers for an ID are just two of the many distractions from that security effort. In your case your background check got you on the ship, not your ID.
On miltary duty you are not a citizen, you are government property.