So this whole question, Keltham admits, is not something he has actually given much thought before. There is of course no standard rationale you're told in Civilization for why the Keepers and Governance couldn't possibly be corrupt - that's ridiculous in the light of elementary Security reasoning, obviously, if you're inside a Dark Conspiracy, any standard rationale like that you get, will be corrupt. Any dath ilani who wants to reason this out should do that on their own or with a few personally-known trusted friends, obviously. Probably even a Dark Conspiracy wouldn't think it could get away with having standard social beliefs and arguments about how they couldn't possibly be ruling society from the shadows; individuals would be smart enough to reinvent the incredibly simple argument from 'security-mindset' about how no such standard arguments should exist, and that actually would be a giveaway.
It's an unduly fascinating question, which Keltham should really extract himself from, and get back to his original intended lecture topic, which was the forms of Governance.
He's totally not going to do that and go on talking about this anyways.
So! On a few moments' 'first-reflection', it seems to Keltham that estimating the probability of Civilization being run by a Dark Conspiracy boils down to (1) the question of whether Civilization's apparently huge efforts to build anti-Dark-Conspiracy citizens constitute sincere work that makes the Dark Conspiracy's life harder, or fake work designed to only look like that; and (2) the prior probability that the Keepers and Governance would have arrived on the scene already corrupted, during the last major reorganization of Civilization a few decades ago. Keltham basically doesn't think it's possible for criminal-sociopaths to take over Keepers and Governance that start out actually functioning the way they currently claim to function, nor for criminal Conspirators to successfully conceal a major Conspiracy from a functional society not run in toto by that Conspiracy.
With respect to point (1), Keltham would first like to observe that a tyranny like this - he uses the Taldane term 'tyranny', it's shorter and feels like it has more of the right connotations than the nearest Baseline term - doesn't seem like it could most effectively secure its power by electing to construct a veneer of Civilization and hiding behind that? Where that veneer involves raising the non-Conspiracy kids knowing enough Law that they won't submit to threats, want to overthrow Conspiracies, and know mathematical protocols they can personally verify that sure seem apparently useful for overthrowing Conspiracies?
A more sensible tyranny should try to have a population of technically literate but obedient order-followers, frightened of retribution, knowing how to do chemistry but not knowing the Law of 'decision-theory' whereby they could try to coordinate with each other or that would make it obvious they should ignore 'threats'. Law-knowers who start out in a world of threatenable people, which makes it be not a 'threat' but only the ordinary optimal strategy for the Tyranny to kill any Law-knowers, will find it obvious that they should conceal their knowledge and wait for opportunities to strike. But Civilization is a whole society of Law-knowers, and those will find it obvious that they should all coordinate in shouting 'NOW!' and ignore threats past that point.
This seems, to Keltham, like not the optimal way to arrange a tyranny that wants to hold power and exercise as much power as possible? Such a tyranny should restrict knowledge of Law to a tiny clique of the smartest people who are allowed to know how the Law of Coordination works. It should run heredity-optimization at a level where it's not trying to make the average people as smart as an average dath ilani, maybe more like Intelligence 14 than Intelligence 16-17, and the tyrants form a separate group with heredity-optimization for much higher 'thinkoomph', the equivalent of wizards-with-headbands compared to Intelligence 10 people.
This, obviously, is not what Civilization looks like! Keltham can observe that just from direct introspection on how smart he is!