Upon rereading his comment, it still does not appear to me as though he is attempting to prove anything. He is merely displaying a healthy suspicion of something which, unlike Russell's Teapot, is fairly plausible.
Furthermore, his point is logically sound: In a world where governments are permitted to keep secrets, they are effectively able to keep secret what they are keeping secret, by simple induction.
Furthermore, his point is logically sound: In a world where governments are permitted to keep secrets, they are effectively able to keep secret what they are keeping secret, by simple induction.