Unfortunately neither the fans who suggested the myth, the researchers, nor the build team have understood contagious disease.
If the corpse was contagious enough to use as a biological weapon, it would also infect the army throwing it.
Apparently the researchers didn't do their jobs when it came to castles and medieval warfare.
Medieval armies wouldn't waste their time catapulting corpses over the outer wall, since they'd know no-one would be all that bothered because they'd be in the Keep. Depending on how well manned the castle was, they might not even notice.
The Keep is the strongest, most defensible part of the castle where everyone goes during a siege, and there's generally enough space for a small town between the outer walls and the Keep.
(The attacking army would also be more worried about the smallpox or plague outbreak in their camp.)
The catapult was invented 800 years before the medieval armies were supposedly using trees.