Most sane conspiracy theory is an historical investigation into the hidden forces in political events
How accurate 'Yes Minister' was, and how this has changed in the meantime, I cannot say. We are given to understand that the Blair years brought in a more presidential 'spoils system', which hemmed in the mandarins. Nevertheless, within the premise of the show are certain facts or assertions that hardly anyone would deny, ergo; that government, in its broadest sense, is big and sprawling, suffering poor communications, is nothing like as efficient as it would have us believe on the outside, and is institutionally secretive, to the extent that the default position with regard to anything likely to cause scandal is; bury it. Additionally, the truth was always multi-layered. Let me give an example:
Hacker makes a public announcement of a bold new policy. Sir Humphrey is furious as it's the first he's heard of it, and the policy is directly contrary to his own interests, so he sets in train a plan to assassinate the policy, or more precisely he must convince the minister to sign the policy's death warrant. Through various underhand means and his extensive network, Sir Humphrey spins a web, entrapping Hacker amongst the vested interests Sir Humphrey is defending, and before he knows what's happened, Hacker's desired-for policy is transformed into a gun pointing at Hacker's own head.
At the final point, all he really needs is a story to tell the public. All he really cares about is what the papers write about him. Sir Humphrey knows this well. It is often the means by which he can entrap Hacker. Sir Humphrey always wins because he always offers Hacker a way out, having previously ensured that there is only one exit available.
What the audience see is that the real reasons given for a change in policy are not those mentioned in the press release, and that there are other forces operating than the politicians. It can be used to support the so-called 'cock-up theory' of politics, that the politicians aren't anything like as all-seeing and all-knowing as they may pretend. But it also supports the 'conspiracy theory' of politics, that they are merely one piece on the chessboard.