Fan films would just get the fan sued to Hell and back by Warners.
Warner Brothers & Babylon 5 = Catch22 & Monkey/Nut/Jar.
My first opinion is to say you're right. That said: "Star Wreck: In The Pirkenning" is 50% Babylon 5 fan film. As far as I can tell, Warners never gave it a second thought.
Not that they could do anything about it anyway. Parody is protected as free speech. But no one seems to have had their hackles raised or even noticed. I was friends with some of the Star Wrek crew, and AFAICT, they never even got a C&D from Warners.
From a legal point of view, EVEN IF THEY KNEW THEY WEREN'T GOING TO WIN A SUIT, they'd still send out a C&D simply to establish a legal history of protecting their copyright. They have to, otherwise opponents can argue "You really didn't care," and that makes future lawsuits problematic. Warners *APPEARS* to have done nothing.
This is odd, honestly. Either they didn't notice at all, or else they just consider B5 a dead property not worth hassling about.
Honestly, if I were gonna' try to make a B5 fan film (Which I'm not), the first thing I'd do would be to contact Warners and simply ask them if I could do a "Star Trek Phase 2" kinda' thing with their property, and point out what that did for Trek. I'm assuming they'd say 'no', but given that they couldn't even be bothered to sue someone about it in a high-profile situation, ya never know.