Well, he did serve. He signed up for extension courses for the Army, in 1937. Then was in the reserves IIRC, until 1942, when he went on active duty.
It was his dream to serve overseas, but his bad eyesight prevented it, so he worked in the film industry making war films.
He ended up as a Captain in the Army Air Force.
(I just read all this last week somewhere.)
Bad eyesight? He wore glasses?
BTW, I just found out a lot about him last week, too!
I heard that he actually lied about having decent eyesight just to get in to the military.
Compare this to bill clinton's letter to the draft board.