I personally know of two cases where light aircraft were indeed shot down.
About 22 years ago one of the guys at our airport was taking off to the East in his homebuilt Varieze. The runway sticks out into a body of water in that direction. Soon after takeoff he experienced a severe vibration, did a 180, and landed on the runway downwind, overunning the pavement onto the grass at the far end. Examination showed that the wooden prop was shattered and there were shotgun pellets embedded in the cowling. It appears that someone in a boat had fired at him as he flew over. The cops did find a man in a boat on the water but there was no sign of a shotgun.
In my home town of Columbia SC there was an earthen embankment in the woods where everyone would go to shoot. The pattern of the local airport went right overhead, about where airplanes would turn from base to final. I wondered if that would ever cause problems. Then in 1975 a guy was flying a homebuilt Breezy in just about that location when a large caliber round struck the bottom fuselage structural member and broke it, and I think it took out the prop as well. The pilot barely made a safe landing.