Surely copyright law isn't that difficult. Every person owns the copyright to everything that they make, even sans registration with the LoC. Okay, so the designer does retain copyright, provided that it wasn't work-for-hire.

There is no contract between the designer and the design company. And from what he says, he didn't get paid to develop on an hourly rate which means that it's not work-for-hire. And he hasn't been paid, which means that there wasn't an implicit contract or a verbal one that culminated in payment.

That means that the design company won't have any proof that it originated the art (and thus would have copyright of it), nor will it have any proof that it purchased or licensed the art (and thus would have some rights to use it). The designer could likely produce many design iterations that might be quite convincing to a jury that he was in fact the person who generated the designs.

Of course there's no way to be sure that the FBI would take the designer seriously. He's just a "normal guy" and his adversary is large and probably well funded. But that doesn't mean that the "normal guy" is wrong.