I think that would hold up in court. Having a written statement saying they committed a crime, and then finding the file would probably be enough in most courtrooms based on my experience. Would vary by judge/jury, but that would be enough for most IMO.
They said they downloaded it illegally, are tied to that statement by the signature on the check, and a search proved that they did have a copy of the file.
That's going to be enough to sway most judges/juries that they did obtain a copy of the file illegally.
Plus, if the OP isn't a wimp, he'd stick to his story that he downloaded it illegally to protest the pricing, even in threat of legal action.