Under the first amendment, Fox has the right to criticize the President. Under the first amendment, the White House has the right to criticize Fox.
George W. Bush's first press secretary was Ari Fleischer, who called reporters whose stories the White House did not like. Reportedly he threatened some with loss of access to White House sources in the future. If you are a White House reporter and cannot get access, you could very well lose your job. In my opinion, Fleischer's threats crossed the line. Can anyone truly say that the actions of the Obama White House have crossed a line?