The only surprising thing here is that the studio did figure it out. It probably took twelve hours for one of the lawyers who knew what a shitstorm of trouble they were about to get in to find the right executive and convince them to back off.
There is no copyrighted work to infringe here, except -- I am not making this up -- the fan video. There is no Tolkien story to infringe whether you own a blanket rights package to his works or not. You cannot copyright a name like "Gollum" or an idea like "let's tell a story about looking for Gollum after the trilogy." You can only copyright the expression of an idea, that is an actual, completed story. Tolkien never wrote such a story, and neither has the studio. Guess who has? The fan video guy. He doesn't even have to have registered it. In the US copyright issues upon creation of the work. Registration just gives you the right to countersue for punitive as well as actual damages.
The studio was setting itself up for a massive, embarrassing loss if it pursued this even one more millimeter. It's a stark reminder that these multimillion dollar corporations do not, in fact, own everything (at least not yet). And that is exactly the sort of reminder those corporations probably do not want to drag out in front of a bunch of TV cameras, ever.