Well, lawsuits have multiple stages. First the plaintiff files the suit, and serves notice to the defendant(s) that the suit has been filed. Then there's a period where both sides gather evidence (discovery), then there's a trial where they present their evidence & arguments to the court. Each side gets time to respond to the arguments made by the opposing party. Then a verdict is chosen, and any penalties are decided by the court. So there's not really any chance the judge only hears one side of the story.

That said, I think we do agree. The plaintiff should be prepared to refute a fair-use argument raised by the defendant. I'm just noting that the refutation doesn't need to be part of the initial filing, it gets presented at trial, after discovery, and only if the defendant presents a fair-use defense. So they don't have to prove it's not fair use to win in every case. I'm probably also being excessively pedantic!