Personally, I liked that trailer, whether it was fan based or not.
I use to watch the TV series 21 Jump Street when it started all the way through to the end, then they made the movies... as hilarious as they were, they totally fucked it all up, they went from semi realistic crime fighting (TV series) to just Dumb & Dumber comedy, it was a disaster for me personally.
Now, this trailer is the exact opposite from the TV Show, so what is your problem that they went this way for A movie? It gives more depth, well, if they do it right that is... also, they need to understand that Jazz is from Wills past, not someone who introduced himself in LA at a record store (well, I may have missed this TV episode, but I always thought they were childhood friends from Philly).
I would watch it.