Generally speaking, if you protest the copyright claim under whatever reasonable fair use claim you can make, the douchebags will back off.
For example: A friend of mine made this credit crawl video:
He actually has made several, each of which has been copyright claimed, the copyright claim has been overturned, and he's sent me a link to a playing of "I Fought the Law" by The Clash with the title "They fought the law, and the law won."
Fox Media had it removed for violating the copyright on the 20th Century Fox Fanfare. Later, someone else made a claim about the music. In both cases, he claimed that it was fair use under parody law. The Fox Logo is parodied, but the credit crawl, while technically a parody under law, was not intended to be humorous. That said, parody law is rather non-specific. If somebody could find humor in the content, usually it can be considered parody In both cases, the copyright violation claim was retracted. (Though Fox took the maximum legal amount of time, 29 days, to retract their claim.)