Never heard of a fighter pilot thinking he may have shot something down and not claiming a 'kill'.
I believe the wrekage of the aircraft was found a few years back and there was no evidence of gunfire. However, there is a theory that his death was suicide following claims by the Free French that he was some kind of traitor.
His death was in any case a great loss if for no other reason than the fact that he had other great books still to write.