I heard on Fox that the President does have the power to fire and appoint a successor
That would be like saying the President has no right to fire the Secretary of Defense or anyone else he appoints. I remember when Nixon got in trouble politically for firing the Attorney General but he could still legally fire the man!
My guess is that the Obama camp sent them the (false) information and the FIVE MORONS did not even do a simple fact check before squatting out this pile of dung.