There was an interesting article in Aeroplane a few years back by Carmichael's wingmen
He said that of his four-ship all fired their guns in anger in the general direction of the enemy and in the mêlée no-one was certain who had administered the killing blow to the MiG, Carmichael still had enough 20mm to do a practice strafe on the way home so is unlikely to be in the frame. His explanation was that the Admiralty needed a hero to present to the great British public so Carmichael was chosen
Still, fair dos, taking out a MiG with a Sea Fury's quite a thing