My overwhelming impression, honestly, is that Chiyoda in general is putting up a massive facade, trying to portray themselves as significantly more powerful, more omniscient, more well connected, etc etc than they are in reality.
They're trying to put together this image of effortless grace and competence, but it's starting to fray a touch at the edges when it comes to an extremely powerful outside group like ours suddenly and unpredictably barging in.
This shouldn't be that surprising - the kind of brute force power it would take to keep something like Tokyo in check is many orders of magnitude greater than the amount of power it takes to run Tokyo through, well, politics -
well placed information gathering, playing internal actors against each other, and so on.
This also, it has to be said, doesn't make them bad people. "Not being strong enough to hold Tokyo with brute force" is hardly a sin, and keeping Tokyo stable through guile, misdirection, and a silver tongue ultimately saves just as many lives from magical girl combat as doing it the direct way.