If results such as theories of geometry were faked by Europeans during the Renaissance, then those Europeans were even more ingenious than as credited today. Either way, a win for them.
Archimedes' discovery of the law of buoyancy in the bathtub is indeed unreliable, most likely similar to the apple hitting Newton's head, and shouldn't be taken serious.
But Archimedes' lever for moving the earth is indeed very suspicious since it requires knowledge unlikely available.
