Actually, he may have a point. Paul went into this knowing that the film was a derivative work of a third party's copyrighted material. One would presume he'd also know about the Guidelines, which explicitly prohibit the filing of such copyrights. Furthermore, Axanar would presumably be a derivative work of Prelude to Axanar, for which Alec Peters was a co-writer and has a story credit for. So any copyright Paul could file would be a derivative work of both CBS and Alec Peters (strange as that may be). And, legally, he'd have to disclaim the portions of the script that are derivative when he files the copyright. So he'd not only have to argue the validity of a Star Trek fan film copyright, but also that it's valid without the consent of the co-writer of the fan film for which it is an obvious derivative work and whom enlisted his help to write it in the first place. That seem like a weak case to me, even with a "Copyright 2020" notice. It's not like adding that creates a copyright license from anyone who reads it. Besides, I'm not even sure modern copyright law requires a notice anymore. I think that's just a hold over from earlier copyright law.