This is what I think happened. Sky have first choice and are always going to pick Manchester United. They picked the Chelsea and Manchester City matches because they have new managers.
BT are left with a choice of Liverpool v Stoke, Arsenal v Aston Villa, and Crystal Palace v Tottenham. (Technically any of the other 4 games could be picked, but were never going to be.)
BT I think choose Liverpool because, Liverpool are the 2nd most rating team in the League, and it would be a while before they can show either of Liverpool or United if they don't select one of them now.
Crystal Palace v Tottenham is then chosen because its a new team from the championship playing one of the big 6 at home.