Glowlight- I find it hard to believe that a letter from ballet teacher would make a difference unless your teacher is widely known and respected.
I know for a fact that there is some direct communication between some JA teachers and Miss Stock, but I suspect they don't have an influence over the final outcome.
I just imagine she sits there with a huge pile of photos and has 3 piles a yes, no and maybe! It is fun, but probably pointless, to speculate. And it does seem that children who apply on more than one occasion can get a different response each time.
Sometimes the children that come in from the waiting list are the ones who go on to get invited to audition for the school or win prizes, so it is obviously far from infallible.