I think you've missed the part of "You don't have people on Corinth." The agreement of you using Corinth as per the role play, is that until you work out terms for a monthly contract, you have no one there. Not to mention as per this thread it at least comes across that you took all your people back to Ames.
So, unless something has changed, I don't see why you have any involvement with Corinth until there's some form of RP around you having anyone there. Until you've done that, I would request 0 mention of Corinth.
Also, OSI which is also a Zoner faction, does not have access to capital vessels. It was more a curiosity than it was "you shouldn't have them." If anything, it makes sense for the Nephilim, just in my personal opinion, not the Aquilon as much. Either way, makes sense.