Well, this is all clear as mud. The original one-sentence statement from Erika Lippoldt is anything but self-explanatory, and all the speculation based on it is sheer guesswork. Kurtzman's (seemingly) contradictory statement in his own interview is equally ambiguous.
Let's everyone keep in mind: writers are not lawyers. Odds are what we have here is the equivalent of a giant game of telephone: EL has heard there was a corporate split between CBS and Paramount, and she knows someone up the pipeline from her has told the writers' room "don't use elements XYZ," and she's inferred a connection... but she
doesn't know the details of IP law nor any specific contractual constraints involving any specific characters or concepts (nor does she have any reason to), so when she mentions "the rights issue" without saying what it is, that really tells us nothing. To the extent that fans now base additional inferences or assumptions on her statement, that's just extending the game of telephone even further.
Here's what I (think I) know: CBS owns all the IP (intellectual property) associated with Star Trek — or at least, all the
copyrights, although perhaps an ancillary trademark here or there belongs to someone else (whether Franz Joseph Designs, Bad Robot Productions, or whomever). Note that trademark basically just refers to distinctive visual iconography... copyright is what's important here, as it covers all the concepts, characters, and so forth. (For instance, Superman's "S" shield symbol is trademarked, but Superman as a character is owned as a matter of copyright.)
This doesn't mean that CBS can necessarily do
anything it wants with that IP, because ownership isn't everything; there are also contracts. Under contract, per the 2005 Viacom split, Paramount owns the Trek films, even though it doesn't own the IP they're based on, and has a contractual license to produce new Trek films. (Similarly, for instance, Sony holds the Spider-Man film rights, and owns the specific Spider-Man films it's produced over the last couple of decades, even though Disney/Marvel owns the IP... so as a matter of contract, until the rapprochement between Sony and Marvel Studios a year or two back, Marvel couldn't use the character in its own Marvel Studios-produced "Marvel Cinematic Universe." Now that the relevant contracts have been renegotiated, it can, but Sony still gets a cut.)
Where Trek in general and DSC in particular are concerned, the logical upshot of all this (unless there are some
very unusual contracts involved) is that CBS can produce new Trek material for TV, but not film... and in that material, it's free to use any Trek-related IP it wants, with the possible contractual exceptions of characters/concepts and/or visual trademarks created for and used
exclusively within the films (such as, for instance, Saavik, Sybok, or the Ryan Church version of the Enterprise). It could probably even use those if it wanted to, with the caveat that doing so would involve paying fees to the current rights holders. What those fees are and what contractual headaches would be involved, we have no way of knowing. (TBH it seems kind of moot to me, as I can't personally think of any movie-exclusive content that would even be relevant to the pre-TOS setting of DSC, but perhaps I'm overlooking something.) Of course, what elements producers may have told the writers' room to steer clear of for various reasons
other than contractual constraints, we also have no way of knowing.
Meanwhile, other kinds of tie-in products (such as novels, online games, etc.) involve rights that are completely separate from film (or TV) rights, and CBS is free to license those out however it pleases.
At least, that's my best guess, knowing what I do of IP law but nothing of the details of CBS's contracts. If anyone has more reliable information, by all means shed some light here!
Meanwhile, on a completely unrelated tangent... from the article:
I think this was something that [EP/Director] Akiva [Goldsman] really liked the notion of. He just kept joking, “Klingons have two dicks, Klingons have two dicks.” And then finally showed it on television.
Puerile as that sounds, it's just about the level of sophistication I'd expect from Akiva Goldsman. Sigh. I have no doubt the entire show would be better off without his involvement.
).