If you step back and look at the situation objectively, there's absolutely no way the BBC would fix this show. Given the "fixing" of other stuff in the past, it's more than someone's job is worth. It would ruin the reputation of the best variety show on TV if it got out.
There's always a high percentage of BBC people in the show, which is only expected. They choose those that they think might do well, there's always a trade off if they can raise the profile of one of their people through their continued progress in the show, but I don't think they really care that much if one of theirs doesn't win, not enough to fix it anyway.
However, the progress of some individuals is not beyond some influence. This can be achieved by selective use of clips in training videos, to hopefully improve the public's perception of them, "in a good way."
I think Emma Bunton was given "every assistance." (She came across like Mother Theresa, always "sweetness and light" no momentary strops, in training clips) before her appearance in the Strictly element of Children in Need that year, even to the inclusion of a visit from French and Saunders to give her support during one of her training sessions. What was that all about?
I've no idea what are the motives behind the judges scores for some people on occasions, nor do I suspect do they have much idea either.