I left a fleet to join another. As soon as I did, I saw 'You have been promoted' a couple of times. I asked why I get promoted, answer from leader: So you have a rank with the ability to invite members.
Its not that everyone can invite. You - or your fleet rank - needs permission.
I used this permission a day later. I saw on the main page that the person wanting to join is online, so I signed on and invited him. In the same moment, the person signed off. I assumed the invite didn't go through, as there was no 'Player has joined' or 'Player has refused' message. Today, I saw he is listed as a member. So technically, my invite came 'offline' - the message 'invited player to fleet' came after the 'player signed off'. He could still accept it. Umm what now? Was it offline? Online? When, what?
Well I know for a fact that I am the owner of my fleet. So rank has nothing to do with it.
I imagine your invite was sent before he completely logged out, with that said someone should try logging in their out of fleet toon first, then quickly switching to see if there is some sort of delay.
Or, better yet, a DEV could post a response as to what is going on...