I think this isn't entirely correct. I think U2 sold the distribution rights of Rattle & Hum to Paramount, but I think they own everything else related to R&H. Keep in mind that U2 financed the movie themselves and only went shopping around the various film studios after the movie was shot and edited. They presented the final cut, film studios had no influence on that. So in that sense I think that U2 own the rights to the footage (also, on the VHS release of The Best Of 1980-1990 they included a video of One Tree Hill shot during the R&H filming).
Hmmmm. I'm not so sure about that. R&H among my favorites, and I've followed this pretty closely. My understanding is that U2 initially intended to finance the film themselves, and just distribute it as kind of art house film. But when cost started to skyrocket (it was budgeted at around a million, went over 5 million+, which was a lot to them back then), they sold the rights to the film to Paramount, including most of the existing footage, for around the 5 mil they put into it. Once Paramount got involved, it became the wide release, heavily promoted film we know today. And I don't believe the film was complete when Paramount bought it because Larry and Edge in particular have made some comments about needing to change the tone & purpose of the film for a widespread release (the interviews, etc). And they definitely had a wide release in mind when they were editing it. Some of this is described in McCormick's book.
And I'm almost certain Paramount owns rights to the bulk of the raw footage in addition to the completed film. For one, McGuinness said as much in an interview (it was with a music business trade pub if I'm not mistaken, but I can't remember which one) about the time U23D came out that the band tried to buy back R&H from the studio but couldn't come to terms. Part of the rationale was he said U2 would like to use new and existing footage for some future release. But film studios are notorious for not letting properties go, and in any even they know U2 has deep pockets now and would likely demand a mint for them.
For another, it would be a very unusual business practice, by Hollywood standards, for Paramount to buy the "finished" film but not the rights to the unused footage. As far I know, it wasn't just a distribution deal...Paramount essentially bought R&H for the 5 mil U2 put into it. In any event, I'm certain that selling the film to Paramount is something U2 regrets now.
The problem is that the movie was shot on low grade film stock, which was common for concert films of the day. They just couldn't afford to shoot thousands of hours on high grade film. So if we are EVER going to see an expanded R&H with new footage (or new, completed footage in any form), someone is going to have to do a proper restoration on it. Which is expensive. And there's no indication Paramount see's an economic incentive to do it (they didn't even bother to do a new transfer for the Blu-Ray release), and apparently U2 is not expressing any renewed interest in buying it back.
Obviously your correct that U2 owns all the songs from R&H and anything that appeared on the album. I'm not sure about the One Tree Hill video, but that was likely just authorized from Paramount. But the film and footage itself I'm pretty sure still belongs to the film studio, unless something has changed. But I could be wrong about my timelines of the events, so if you have anything that contradicts this I'd love to see it.