Counterexample:
http://cyberlaw.stanford.edu/documentary-film-program/film/a-fair-y-use-tale
A short film explaining the concept of fair use that was cobbled together entirely from clips of Disney movies.
That's not a collection of copyrighted works for the sake of it, that's using a copyrighted works to illustrate the discussion about fair use.
One could well consider BJAODN as an example of parody, in fact. :)
A parody of what? "parody" doesn't just mean something funny. It has to be a parody of something, and then you can use that something under fair use. BJAODN would have to be a parody of itself for that to work, which is obviously nonsense.