In 2007, Universal Music Group sent a letter demanding that a video of Stephanie Lenz's toddler dancing to Prince's "Let's Go Crazy" be taken down from YouTube. YouTube complied, but this was not an open and shut case.
Lenz teamed with free speech advocates to get a judge to declare that her video was a fair use of the song, and since then, she has sought damages against Universal for sending a meritless takedown request.
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How's this for a moral: if a claim seems a little too ridiculous, maybe it is.