Captain Greer was the pilot in a F-82G Twin Mustang night fighter with the 68th Fighter Interceptor Squadron, 6160th Air Base Wing. On 27 January 1951, he failed to return from a combat mission. He was listed as Missing in Action and was presumed dead on 31 December 1953. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

For his leadership and valor, Captain Greer was awarded the Distinguished Flying Cross, the Air Medal with 3 Oak Leaf Clusters, the Purple Heart, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.