I just want to add to this that if GRG wants to use Corinth, they can use Corinth.
OFs represent npc factions, they do not own npc assets. In this light, and if the lore supports it, GRG has as much claim to Corinth as all other Zoners do.
Same for the Zoner caps. Their ID allows it, so they can use them rulewise.
(But please do not overdo it. I personally try to support all our ships with lore backing and RP)