CBS can neither prohibit nor authorize any matters involving copyrights that aren't actually theirs. And while CBS holds the copyright to the overall Star Trek property itself, the rights to anything that's JJ-verse specific is held, not by CBS, but by Paramount and Bad Robot. So when CBS says that they simply will not permit fan-film use of the JJ-verse, it's likely that what they're really saying (in a round-about legalese fashion) is that they can't give you that permission as it's not actually theirs to give.
What defines the "JJverse" in legal copyright terms? It can't be the characters, because you can always say these are based on the original ones.