It's not something I'd bet the house on, and it probably is presumptuous. But moronic? I think that goes too far.
When Desilu gave Gulf + Western ownership of Trek, Trek was a badly failing first-run TV show about to head to the Friday Death Slot. When G+W spun off Trek over to Paramount, Trek was a pretty solid syndicated TV show with two movie sequels with no third in the works. It's not at all difficult to imagine some corporate lawyers not paying adequate attention to the transfers.
Of course, after that, Star Trek was indeed a big deal, but it's changed hands quite a number of times, and copyright transfer between giant media conglomerates is a complicated legal maneuver. As anyone who's worked in a big company knows, things get lost in the shuffle and not discovered for years. All Axanar needs to find is one error at one point in the chain of copyright custody, and it can bring down the whole copyright claim. It's not crazy to think they might. Such things have been discovered from time to time before.
On the other hand, CBS/P has undoubtedly taken careful stock of its copyright chain-of-custody by now, and, if they were vulnerable, they surely would have discovered it by now and settled the suit for fear of that evidence getting out. So I'm betting they produce the documents in open court and everything is in order.
Just FYI - Gulf+Western picked up Desilu in February 1967 <--- At that point Star Trek was just halfway through it's first season.
Also, Star Trek BECAME what it was BECAUSE of how Paramount aggressively syndicated it (they spent a lot of money - they wanted/hoped to see some return on investment.)