The thing about Pokémon in particular with fics is that there's a heck of a lot of room to work with, a lot of gaps to fill in, that really there's not too much to copy. Sure, you get the generic trainer fics where they copy how Ash goes, or the games go, but there's a lot more.
You have now over 700 different critters to write about; how they act, how they live, etc. A bunch of pokedex entries exists, and movesets/their basis on real-life animals/objects provides a bunch of info, but there's still a lot to play around with.
Or the canon human characters. Take your typical gym leader - you have usually at least some general personality provided, what type they like, but you can come up with so many 'what if?' situations with them. And so forth. Pokémon tends to provide the characters and a slew of settings, but there's nothing too hard and fast about it beyond the general battling system and vague roles that only have become more refined gradually. And that's ignoring that there's three separate mediums you can choose to base your story on as well!
Besides, fanfics do help promote the brand, and let people explore different ideas and views on an aspect (or few) of the franchise. There is the odd author/creator who doesn't want people to write fics of their work, but Pokémon isn't one of them so I'd say they're fine with it. As long as you're not trying to profit directly from their work, anyway.
