@CCMan1701A has a point. The model was built for production purposes, so it would have almost certainly been paid for - and therefore owned - by either by Desilu Studios or Norway Corporation (aka Norway Productions) depending on how the accounting was set up back in 1964. So unless Desilu/Norway sold or gifted the model to Roddenberry at some point, ie formally passed title to him, technically it would still be the property of the original corporate owner.

What I think quite possible though is that after TOS was cancelled Roddenberry took possession of a bunch of production assets nobody ever thought would have any value. Star Trek, after all, was a failed show. IIRC it was known that he used to do stuff like that, eg selling off merchandise to fans that - technically - he didn’t own. It’s just that nobody really cared too much back then.

Now as it so happens, Norway was actually Roddenberry’s production company, but technically that doesn’t matter, as there’s a legal distinction between a corporation you own on the one hand, and you as an individual on the other. That’s the whole purpose of setting up businesses as separate legal entities. So even if the model was originally purchased by and owned by Norway (as opposed to Desilu, which was sold to Paramount during the show’s run) then Norway (Roddenberry’s company) would still have needed to pass ownership to Gene Roddenberry the individual (via a gift or sale) in order for Majel Roddenberry’s statement that “it was Gene’s” to be strictly true. Of course, that would have been a cinch to do: Roddenberry, as owner/executive of Norway, simply sells or gives the model to Roddenberry the individual.

It’s possible that this happened, ie that Desilu or Norway sold or gifted the model to Roddenberry, but it’s also possible (especially if the model was owned by Desilu/Paramount) that he merely ended up with it, and that nobody questioned his legal right to it in the years since.

Personally, regardless of whether technically (ie from a legal or accounting perspective) Roddenberry did or did not own the model, I fully understand that Rod Roddenberry would be interested in recovering this seminal piece of Star Trek memorabilia, and I wouldn’t have any issues if it stayed in the Roddenberry family or was gifted to an institution like the Smithsonian.