Don't forget about Rika. From her story we know that she isn't one of the gravity children, but her abilities of the thorn road were the thing that Sora neaded.
I would even add something to metrobluejay theory. I also think that Sora tricked Kilik to help him create SF, while he realy was trying to get closer to the sky regalia. He found out of Rika abilities, so when there was a chance, he got her to join SF. At some point Kilik found out Sora's true motives(or something like that) and that's why he crippled him. That's the past.
The current time: SF is acting this way, because in the past someone(probably Sora) created the whole mithology around the tower, and the Sky King. They are still protecting the Sky Regalia, while everybody is acting acording to the myth of the Tournament and becoming the Sky King. I think, that what is Kilik trying to do is to tell/show Ikki what is this realy all about, and the true puropose of SF. It even would make sense why exactly Ringo is the leader of SF, as she is the best guardian of the Sky Regalia.