I think it has more to do with the panicky disavowal of Trek fans. JJ's fall back to "this film is not made for Star Trek fans." This line does not refer to a narrow demographic of fans, but rather "fans."
Holy out-of-context, Batman.
You missed a word in your quote: "necessarily",
as in "The whole point was to try to make this movie for fans of movies, not fans of 'Star Trek,' necessarily".
Here is the entire context of what he said about making the first film for more than just Star Trek fans:
Improving Star Trek means appealing to more than just the devoted Star Trek fan. "The whole point was to try to make this movie for fans of movies, not fans of 'Star Trek,' necessarily," said Abrams. "If you're a fan, we've got one of the writers who's a devout Trekker, so we were able to make sure we were serving the people who are completely enamored with 'Star Trek.' But we are not making the movie for that contingent alone."
I don't think you necessarily deliberately (overtly) left out that word, but I think in your mind, you so badly want Abrams to be this villain who has an agenda to stomp on 45 years of trek history that you actually think he said "this film is not made for Star Trek fans."