I wasn't a Pixie fan but I knew when they got rid of her last week that Jake would go this week.
I have worked on the tours of other BBC franchised shows and the BBC most definitely is involved in them. The BBC are very protective of their brand name and franchises and oversee all creative content to ensure their shows are being properly represented. On the shows I have worked on the BBC had to sign off on all creative content, they had to approve of all venues, they had to approve of all the content in the programmes, they had to approve of all merchandise to be sold. Although there is another company organising the live shows the tour represents the Strictly brand, provides excellent cross-promotion for the television show and also makes money for the BBC. If you look on the website the BBC logo is there alongside the other two companies involved in the tour.
I'm not saying the BBC fixes the phone vote (that would be ridiculous) but the negotiations for the celebs to go on the tour begin once voting figures have been established so the parties involved have a good idea how things are going. The companies involved of course want the best chance of ensuring the winner is on the tour so it would be strange for them not to request that the passage of the tour celebs is eased to the final when the franchise deal is haggled out and of course there are ways that the BBC can help this. Jake was at the bottom of the leaderboard last night (perhaps deservedly so) and for the first time this series there were no ties on the leaderboard meaning, even if he was high in the public vote, he was going to struggle to avoid the dance-off. They also have the dance-off and the judges' vote to ensure the producers get the final say. We also know that creative decisions plus things like running order (especially when the phone vote opens during the actual final) can have an effect on the vote.
I'm not saying the show is definitely biased in the tour's favour but we do have to ask ourselves how, after its inaugural year, the tour has had the amazing luck to sign up all the winners and many of the finalists without a crystal ball.