Regional police forces could be a part of the Caldari Navy structure.
Because of how tightly intertwined certain corporate holdings might be, there could exist a need for an impartial logo-transcending force of order. As long as crimes remain confined to a single corporation, the corporate security force has jurisdiction of the case, but as soon as an incident transcends corporate domains or occurs in a grey area (what corporations had jurisdiction over occupied Federation space? None of them until the development rights were sold, thus the State as an entity must have held them in some faculty - and the Navy would have had security authority) the regional police steps in to sort things out.
It's just like the Business Tribunal. The corporations have their own internal legal systems and even courts, but as soon as an inter-corporate issue arises the State can step in an invoke superior legislation.
All in all, I think it'd be more similar to how the Republic might work than the Federation. In the Republic you have seven tribes that may exist separately or intertwined. They have their own judicial systems and internal structures, but if issues overlap they can turn to the Republic for a higher set of authority to straighten things out before conflict gets hot.
Regarding the diplomat, I originally took him to represent one of the megas (just that Abby decided to leave it unnamed). However, it's possible the State could step in to seize control of occupied infrastructure without any Megacorp claims. The term "diplomat" might just be what the Gallente considered him - he himself may have been something more akin to an administrator or executive serving the provist government under the CBT and CEP.
The state thus goes in and claims stuff, sends in their own specialist governors, structure their acquisitions, and then sell the assets to the megas. I believe there are people who do the exact same thing in the real world - acquire failing companies and either get them back on their feet or disassemble them, and profit from the subsequent sales of the result.
This particular "diplomat" may have originally come from one of the megas and had administrative experience from there, or he could have completed previous restructuring and retail invasions of other mining colonies for the benefit of the State.