This is the first time I’ve read of a man in a parachute downing an enemy plane but I have read of a number of men who shot down low flying enemy planes with a single rifle shot. I seem to recall reading about a soldier/marine on either Guam, or Wake that brought down a low flying Japanese plane with his Thompson submachinegun.
I read about a German tank crew shooting down a Mustang that was strafing them with a round from their main gun.