Last summer, DC Comics and Warner Bros. cracked down on a bunch of shows in the audio drama world, not for using their intellectual properties (Batman, Superman, etc.) but because those shows were using tracks from released soundtracks in their audio dramas.
Paramount hasn't done anything like that, it seems. Hidden Frontier aped all kinds of stuff from the GNP releases over the years for their shows, and to my knowledge (which is, admittedly, limited on this topic) they were able to get away with it.
Sometimes those things get shut down by the companies who paid for the rights (for instance, Atari famously sued Tandy for a PAC-MAN copyright violation even though Atari didn't own the game, but had purchased a license to publish it), or the ASCAPs of the world who are protecting composer and musicians rights. Not saying this is the case with Star Trek, as I've obviously no exposure to whatever contracts are in place, but rights related to movies and TV are often a lot more complicated than people realize.