Baseball is far more random than any of the other major sports, and I think that most people do not realize how much randomness affects the game. In small samples, in short series, and in close games, randomness is king.
I suppose there is no definitive proof that Schilling's postseason performance is all randomness. There is no definitive proof that clutch does not exist. Only very, very strong evidence. The correlation between clutch from one situation to the next, be it from game to game, month to month, season to season, postseason to postseason, etc., is nil.