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I agree that some clubs acquire a negative media narrative - but each for their own unique reasons. For example, if we say that Newcastle and Stoke are the victims of a biased, London-based media, what do we make of those same scribes' treatment of Arsenal? Arsenal have been a target for years due to a growing media narrative (based, I think we have to admit, on at least a kernel of truth) that things were getting stale under Wenger - with the added side story about Kroenke's ownership and the notion he is happy to keep Arsenal a profitable, thoroughbred also-ran for as long as he owns the club.
Similarly, Newcastle continue to labor under the ownership an execrable tycoon. I don't see these clubs as the target of 'cheap shots' in the media - but I do think the media call out the club owners and suits pretty often. And I don't see anything wrong with that.
Stoke were a victim of their own success - when you can't compete financially, you adapt your playing style to your resources and under Pulis they became horrible to watch and even more horrible to play against. But it kept them in the top division for years and, while it is an oversimplification, it is not ridiculous to say that they got relegated in part because they stopped playing like "Stoke on a cold, wet Tuesday night".