Actually, the burden of proof would be on the school to prove that the coach did give favorable treatment to the kids that prayed with him, not to prove that it didn't happen. I expect that if it had been proven that he was giving favorable treatment to the kids that prayed with him, the the court case would have gone the other way, as it should have, but it didn't because proving that he showed favoritism was not part of the case..
To make an analogy, it's Okay for the coach to wear/display a cross necklace while coaching the kids. It's not okay for him to show favoritism in his coaching to kids who also wear cross necklaces. If some kids decide that want to wear cross necklaces because the coach does, then so be it.