I believe that's correct, but there is a distinction. An airborne force is invading, it is inherently an offensive active, even if dropping in support. Pilots shot down are not.
I think that is the correct distinction. There have been "customary" laws or traditions of warfare that shooting soldiers/sailors/airmen in distress (e.g. wounded & surrendering/ship sunk/bailed out pilot) are not legitimate targets, but often observed in the breach. In WWII the US fighter pilots tended not to shoot at Germans they had just shot down, feeling it wrong (and also perhaps a waste of time and dangerous if there were other German fighters about). The Germans generally, but not always, did the same. The Japanese on the other hand did not seem to have any regard for that particular tradition, and I suspect US pilots probably reciprocated.
An actual international Geneva Convention-type agreement that shooting airmen descending in parachutes from shot-down planes did not happen until well after WWII.
I'm not sure about the state of international law for naval equivalents (i.e. sailors in the water from a sunk warship), I was an Air Force guy, not Navy. I know in WWII a German sub got bombed while trying to rescue survivors of a ship it had just torpedoed, which pretty much put a halt to the German Navy ever trying to save survivors for the rest of the war.