Rulebook, p.8 (emphasis added):
The outcome of all ties in bidding is decided by the player holding the Iron Throne token. This player places the Influence tokens of tied players on the highest (i.e., left-most) available positions on the track, in the order of his choice.
The Iron Throne Token
The player holding this token decides the outcome of all ties that occur in
the game, with the exception of ties in combat (which are resolved by a player’s
position on the Fiefdoms track) and ties in determining the winner of the game.
Of course there is no reference to the FFC objective cards in the rulebook for the base game (since the expansion came afterwards), but I think a strict reading of the objective card itself (control more X than any other House) combined with the normal use of the Iron Throne token in the base game (breaks all ties in bidding, but not in combat or determining the winner of the game) means that if two players are tied for the most X, the player holding the objective for having the most X cannot score it.
Edit: The only reference to scoring in the FFC rules that seems relevant is on pp.7-8:
In turn order, each player may choose to score one Objective card of his choice from his Objective hand (if the criterion described is fulfilled) ...
In my opinion, this doesn't shed any further light on the issue, but I included it for completeness.