LeMay very much did fly Combat Missions during WWII.
He started on B-17's in Europe, then B-29's in China-Burma, then headed up the B-29's out of the Pacific Islands, then later went on to organize the Berlin Air Lift Operations before becoming SAC Commander ultimately winding up as Air Force Chief of Staff.
One might note he was quite right in his opposition to the Air War Strategy during the Vietnam War.....although he found himself on the wrong side during the Cuban Missile Crisis.
Say what you will, but he was very instrumental in the creation of the US Air Forces Nuclear Deterrent Forces being an early advocate of Missiles as well as Manned Aircraft.
He was controversial to say the least but then most Men of his position were.
http://militaryhistory.about.com/od/...ce/p/lemay.htm