If I'm not mistakened, the Admiral told Kaga that permission from HQ has already arrived. However, Kitakami said that they can only carry out the Provisional Marriage if HQ gave permission, with her way of speaking implicating that permission hasn't arrived yet...
...So, what do you think that ring actually is?
Edit: Re-reading things through, apparently they're treating the [Provisional Marriage] system as just another modernization upgrade and the existence of the Ring is a lie.