Not trying to argue with you at all, but let me relate one of my experiences.

I was trying to J/S on a full aircraft (Bus), and wrote to the Capt to get his permission. He granted it, and I was authorized 'CP' to be on the J/S. The capt I got permission from ended up not being on the trip when I showed up at the aircraft; luckily for me, the actual capt had no problem with me and said 'no problem'. It so happened that a DO was also one of the J/Sers, and I mentioned that I was in a bit of a gray area, since I had A captain's permission, just not the one operating.

The DO told me it didn't matter anyhow, since the Capt's permission is only required for the first J/Ser to be booked... Actually, he suggested that while that was in the intent, it technically was not the letter of the FOM: Note the ** (double asterisk). (currently FOM 2-24)
He showed my the Jumpseat Booking Matrix and said that the interpretation was that while the capt always had the right to deny any or all the J/S, whether in the cockpit or not, J/S admin only is required to have permission for the first cockpit J/Ser. Idea being that the capt could choose to not let anyone into his cockpit, but if he was going to let anyone in, then J/S admin was going to fill up the cockpit if necessary. He said this was meant to make J/S admin's job easier, though an unintended consequence is that once the capt gave his permission to one, he might give his permission to a second also, thinking that it was his seat to offer, but J/S admin might have already filled the second J/S.

Don't shoot the messenger; just passing along what happened to me.