My view is that Kusari lets the GMG keep to themselves in the Sigmas and Okinawa, since the two groups are on pretty good terms and Kusari is busy in the Taus and doesn't want to deal with any trouble in the Sigmas and Okinawa. However, by whatever reason (cultural ties, the original exploration party, previous support, whatever) the Kusari government considers Okinawa part of Kusari territory. It's just that they're ignoring the complications there for now, since there's bigger issues to take care of.
As for whether Okinawa is "officially" GMG territory or not, I'd like to point out that China (PRC) does not recognize Taiwan (ROC) as its own country, even though other countries in the world do. Sovereignty is only "granted" through recognition by other governments. It's also like how Bretonia claims Orkney as a Bretonian system.
Basically, whatever Okinawa was "meant" as, by the developer, has little to do with how it will be treated by in-game entities.
