I also think a lot of it has to do with the sense of personal pride a lot of fans feel when they see that "one of their own" has made it into the industry, or is basically the image of a "local geek does good" - this is a huge reason why Kevin Smith is still a thing, for example.
So once your fandom is reinforced by the idea (faulty as it may be) that fandom can be rewarded with the keys to the castle (or at least a wing of it), that sense of ownership is only strengthened. And eventually that turns into the idea that being a fan is one of the only ways to make something good.
It ends up just being a different flavor of gatekeeping. Less mean-spirited and bold, but still essentially the same thing: You need to trust us to make this right because you don't understand why it's good like we do. So like, if you're not going to actually put us in charge, you need to at least listen to us, otherwise you're guaranteed to fuck it up because you just don't get it.
(this is, basically, a form of entitlement)
A lot of people don't even question the idea that being a fan is a positive when it comes to making quality entertainment. They just accept it as axiomatic fact. And often being a fan has nothing to do with whether or not the storytelling is solid.
But when you come from a perspective that honestly believes being a fan can only make things better, and you already have that sense of ownership, and that sense of ownership is validated by your projecting your own fandom onto another filmmaker's abilities (i.e. "When he wins, I win, because he's a fan like me!") it makes sense that fans would hijack the ownership of a thing and demand they get to put a hand on the steering wheel.
It doesn't readily occur to a lot of us that it's easier (and more fun) to just like a thing (or dislike it) without worrying about how it reflects our idealized childhoods.
