Don't forget how Bowie played ol' Ludwig Van while showing the disturbing Dalí (or was it Buñuel?) film with the eye-slicing before the Diamond Dogs shows.
While it certainly is true that A Clockwork Orange is not the sole source of Beethoven's 9th, I believe he came straight out and said the film was what inspired him to use it, particularly as acompaniment to the disturbing film.
What's this? Another door?