My take on why Airtel added Star Sports First on day one:
After the news of potential TataSky merger with Bharti Airtel, Star TV's stake in DTH shareholding will be reduced and hence control over DTH operations in India will be reduced. So Star had to hit back by increasing investment in another mode of transmission -DD Free Dish. Airtel in turn wanted to show Star who's friend and also boss and acquired the channel on day one so as to not give any exclusive addition to Free Dish. The game will continue and Star will try to continue it's FTA gambit until Airtel gives them some assurance on plans post merger with TataSky. This is just my theory and may be 100% false.