There's no way in the world that I believe Rodgers wanted to keep Borini and the club sold him anyway. Total made up [oops] stirring scum bag press. Rodgers has said many times he has the final say in all transfer dealings. Most people thought he would sell Aspas and Borini this summer and he has.
Indeed, BR said that he has final say on transfer dealings, there is no reason why not to believe him. That said, I don't think he has final say on price of purchases, nobody has, unless he is allocated a budget and he does what he wants to do.