I agree with ross, he (the DoF) is the boss. the DoF sets policy of the direction the club is going to go in a footballing sense, so if the DOF said we are going in a tippy tappy direction we would get players that service that, play formations that service that, pick tactics which service that.
That doesn't make him the boss, he's there to oversea the direction and style of the club's football, it's doesn't mean he gets final say on everything. It's his job to help instill methods and ideas and target players within that structure, but it's still agreeable between the other major staff. Do you think Comolli said in the Summer, right we're going to play this way and these are the players we are going to buy? There may have been some sway with certain signings that were more accreditable to Damien, but there were equally players Dalglish wanted.
It seems more a case of two heads (or more) are better than one, which doesn't always ring true, but anyway. I see we're now looking at splitting the role, so one member of staff concentrates on the admin side of the role and the other on the footballing side. Does that mean we now have two bosses? Nope.