Submissions that came through me had to come with a signed release from the writer or we would shred them without reading them, but I don't know the policy now. But it's highly unlikely that it's because the production is afraid of copyright issues. Gerrold stated in his annouement the desire to take the show to the next level - which is completely understandable. When you can only film (at the most) two episodes a year it makes sense to use the resources for the best quality material available.
As for MS, a lot of people feel that the nurse in the 20th century interacting with Kirk makes it a Mary Sue. Knowing Shirley as a friend, I know she would be insulted by such a notion. She wrote the story to as a way to illustrate to people that Chekov is, in fact, Kirk as a young officer; to explore what happens to the ship when Kirk is absent for an extended period; and to explore Spock - the lengths he would go for Kirk and,well, his social ineptitude. She missed one big issue with the time travel, and when I pointed it out to her she did a major facepalm. I fixed that issue in the adapation I did for Phase II.