Olivia threatens to revoke Vanessa Chandler's press credentials if she publishes a story harmful to Grant, yet White House staff explicitly do not have the authority to revoke credentials without legitimate cause. If Olivia tried this play Chandler would have excellent chances at a very public lawsuit.
The dossier Jake receives states that the leader of B613 "must operate without interference from the executive branch, all while remaining several steps ahead of the the president." Grant's actual method of installing Jake as Director is never quite explained, and given the president is not supposed to have this authority--or even know B613 exists--he could only hope to overthrow Rowan by having the support of the B613 officers. It's possible the agents and support staff did not like Rowan, yet given how independent this agency is supposed to be, it is difficult to believe they would support the overthrow of their leader and installation of a presidential lackey.