Adele is someone who has my respect in the music industry because she has an honest, real voice and unmatched vocal talent. That being said, I'm glad she turned down the Superbowl's "informal offer" and I liked her reasoning behind it.
She claimed that the Superbowl half-time show is not ALL about the music - that there is a lot of running around and a lot of SHOW that goes a long with it. While Adele is a great performer you'll notice she doesn't move around on stage a lot (Even though she still manages to own the stage) and there aren't a lot of spectacles at her shows like fog, fireworks, or troupes of dancers with all kinds of strange props and weird get-ups.
It would make more sense to me if she was someone that made an appearance in someone else's show rather than her having her own show. Like how Bruno Mars and Beyonce appeared in Cold Play's or how Missy Elliott and Lenny Kravitz came on Katy Perry's show.
People have been inviting others to the half-time show for a lot of the Superbowls. (At least the recent ones, I can't remember too far back)
I really can't wait until they reveal who's show it really would be this time's though.