Thank you for the interesting links! I'm well aware of this problem and tried to highlight it:

The phrase is also a convenient tool to clearly and in vivid colours paint something as low status and unworthy of further investigation. A boo light applied to any explanation that has people acting in anything that can be described as self-interest and happens to be few inferential jumps away from the audience. Not only is its use in this way well knwon, this is arguably the primary meaning of calling an argument a conspiracy theory.

We do have plenty of historical examples of high-stakes conspiracies. So we do know they can be the right answer. Noting this and putting aside the misuse of the label, people do engage in crafting conspiracy theories when they just aren't needed.

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But how many here are likely to accept "conspiracy theories"? To do so with stuff that actually gets called a conspiracy theory dosen't fit our tribal attire. Reverse stupidity may be particularly problematic for us on this topic. Being open to thinking conspiracy is recommended. Just remember to compare its probability to other explanations. It is also important to call out people who misuse the tag for rhetorical gain.

Perhaps I should have emphasised this point more.

Looking at the press association example, I think that one problem here is that similar ideas are being blurred, and given a single probability instead of separate ones.

A lot of the theories involving press/politician association involve conspiracy to conceal specific, high impact information from the public, or similar levels of dysfunction of the media. Most of these are low probability (I can't think of any counterexamples offhand); as far as I know either no or a very small percentage of such theories have been demonstrated as true over time.

Different theories involving association have different probabilities. The Leveson Inquiry is providing reasonably strong evidence for influence and close social connections, so the proposition that that existed would seem to have been fairly accurate.

I don't know what exactly you heard described as a conspiracy theory, in the fairly large space of possible theories, but it seems to me that that example is a good case where it is important to review the evidence for, and recognise fallacies (including overestimation of the probability of agency) in a specific theory, rather than decide what classification of theory it falls into, and judge it based on whether theories in that classification are generally "conspiracy theories".

Could you substantiate the claim that those two examples were "rejected as 'conspiracy theories'"?

The trouble is that lots of things have been rejected as "conspiracy theories" and turned out to be true

Bayes!