Both the captain's chief pilot and the FBI had meetings with said captain and explained to him that his authority ended where the FFDO federal badge began.
If and when you try it I am sure you too will get to have a meeting with a couple of FBI agents. They will explain it to you.
Interesting, I'm not aware of the FFDO program modifying jumpseat access, permissions, or authority. ALPA can do nothing except suggest to the pilot that he play nice. ALPA ultimately supports Captain's authority for granting jumpseat access. The only authority that beats the Captain's for cockpit access is the Secret Service. Of course, certain management persons may have similar trump cards at some carriers.