It likely depends upon the copyright holder and how they choose to enforce their copyright. It can get sticky, too, as it's not so much publicity as it is keeping one's intellectual property under their own control. If you just let any Tom, Dick, or Data do what they want with the brand, that's a quick way to lose control over one's property.
For example, in the My Little Pony community, Hasbro has, on occasion, stepped on fan productions. There was a very well made game being produced by a small group of programmers called "Fighting is Magic," that had garnered a lot of attention, and right before it was released to the public as a free game, Hasbro stepped in and issued a C&D.
I'm of the opinion that as long as it doesn't garner too large an audience, most copyright holders can pretend that nothing is happening, but if the production gains a lot of attention, then the copyright holder is forced to crack down on it, or else lose their copyright hold on the property.
Plus, we all remember, way back in the ancient 1990s, when Paramount went on a rampage shutting down any website or production that even mentioned Star Trek.
Just my two bits.