So no story except for all of the other areas that have stories. There is a difference between you are part of the story and you make up the story.
You're misunderstanding.
In movies and some theme park attractions you're watching a story unfold. A perfect example of this is Undersea Adventure. You watch the protagonist express her desires, put herself in danger, and risk everything for what she wants. You yourself are safely in the clam shell watching the story unfold. You sit passively and take in
her story. Just like if you were watching a film.
At Animal Kingdom (and many other attractions too) the approach is eliminated and the protagonist is recast as you. Instead of watching someone else face the Yeti and speed away on a runaway train, you're the one in fear for your life. Instead of watching some random individual go on a Safari, you're actually riding through the African Savannah. Instead of watching a bunch of terrified individuals running away from Dinosaurs, you're the one being terrified.
That's the idea. There's still a story, but you're the one who makes it all real. This same approach is used on (for example) Tower of Terrors. You yourself are the one who have entered a terribly freaky hotel and are now entering the 5th dimension or meeting an enchanted idol. It can be considerably more effective as a plot tool, but it's not the only approach. Look towards Sinbad as an example of a more passive approach working very well.
One of Animal Kingdom's core values is the idea that we should be changed through adventure. To accomplish that it takes you feeling things. Fear, excitement, awe.
That's what Joe means when he talks about creating your own story. They create the environment, but it's your reaction and feelings that fully flesh out the attraction.
I feel strongly the original intent of BK would have been a more effective framework for adventure, but I also feel strongly that Avatar should create some unique and exciting moments too. I don't think if you're looking for it, you'll be disappointed by a lack of story.
That's simply not an issue.