Is Bill Cosby rape documentary protected by fair use?

The production company that made The Cosby Show has sued the BBC (.pdf) over a documentary the British network aired about the rape allegations against Bill Cosby. Carsey-Werner, the production company that is the plaintiff in the case, says that the documentary is infringing its copyright because it uses eight audiovisual clips and two musical cues from The Cosby Show.

Fair use or silencing of criticism?