Has the owner of Star Trek (Viacom/CBS?) published any official position on fanfic?
For example, I believe Lucasfilms have said that they are ok with Star Wars fanfic (excepting any that include a pornographic element), and J.K. Rowling and Stephenie Meyer (no relation) are fine with it too.
OTOH, G.R.R. Martin and Raymond E. Feist are opposed to it (and presumably may take legal action against anyone that publishes Fire and Ice / Crydee fanfic).