Realistically, Giuliani is the Republican's only chance. And as Fox is a Republic propaganda network, they're just looking out for their party.
Murdoch will support whatever candidate from whatever party support his interests. How else could the man go from supporting Margaret Thatcher to Tony Blair?
He's become buddy-buddy with Hillary already.
I think it's more that Clinton has realized the importance of being buddy-buddy with him. If she gets favorable, or at least not unfavorable, coverage by FOX and the Murdoch papers, she'll win the election easily.
Think Ed Koch 77 mayoral race.