For a period the video was up, but with advertisement revenue going to Lionsgate. They were getting revenue from something that was largely someone else's copyright. In spirit, if they think they should be getting money, then Buffy's copyright holders should too.

Of course, neither should automatically be getting revenue, fair use and all.

that's not true - the author of the work should get revenue should they decide to (but only if they decide to). Lionsgate is not the author of the work. Some components of the work are from the copyrighted works owned by lionsgate, but that is due to fair use, and thus lionsgate has no claim on the copyright of the remix containing some of their stuff.

Fair use does not mean no revenue (nor does revenue even come into the argument!).