What happens if fan-art popularizes counter-culture versions of the IP characters, like Zelda and Link doing cocaine or joining in orgies? It's true that fan art is for the most part supportive of the original artist's direction, much like the amateur film in question, but without any control over which derivative works are allowed, the integrity of the game character could be obliterated. Even something as mild as suggesting Link is gay, while not inherently or morally negative, could hurt the image and damage sales of the Zelda games in areas that aren't as tolerant.
Sure, small-scale fan-fiction is impossible to control, but for all intents and purposes that type of derivative work only influences the community that created it and finds interest in it. When it comes to something as high-profile as this film, it becomes much more important that the IP holder has some say in how its characters are depicted. However, in general I think companies should be more willing to grant no-fee licenses to devoted fans since it only builds a stronger bond in the community. It's a shame Nintendo is fighting back against this rather than supporting it and sharing in the attention.