Well. You need to look one step further.
Imagine you own a video game company and you have a franchise going about “Roachie” a psychotic cockroach that has the wackiest of adventures in far out jump and run games ever.
Now someone comes along and makes a fan game of it. No profit. For the comunity, as you say.
And you kind heartedly allow the person to proceed and release the game to a general public.
The game is well received and everyone thinks you are a cool dude and really down with the gamer base, tollerating a fan made game without legal herassment.
Some weeks/month later:
A guy has an idea to make a fan game based on your franchise as well, but this time it takes a different turn. In this installment of the game, Roachie turns into a foulmouth sexist ******.
Blood and gore all over the screen and a nonstop serenade of racial slurs and cultural transgressions.
Of course the reception will not be as well. Feminist groups, religious associations and social justice warriors in general raise a social media shitstorm against you.
And is the funny part: Because you tollerated the first game, there is absolutely nothing you can do about the second…
So, declining a fan made project is mostly motivated for avoiding to set a precedence…