I don't think this is necessarily true. The issues about lack of rigorous assessment/investigation of a plagiarised thesis, incompetent appointment peocesses, the distortion of diversity objectives to serve corporate PR, etc., etc., all need to be tackled by the institutions themselves. It is an illusion to imagine that a media narrative (or, more excitingly, a social media narrative in which we can all be actors) has a central part to play in all of this.
In fact it is our cultural obsession with media, with narratives, that caused this mess in the first place. Everything that should be quietly technical, evidence-based, expert, detailed and hard - such as recruiting the best possible professor from a pool that was maximally open to all of the best possible candidates, regardless of race, sex, disability - is treated as a public-facing performance of virtue, and of the kind of happy-ending tragic narratives that are spun for us in every episode of a million reality-style TV competition shows.
The solution isn't for Cambridge, Liverpool, etc to be 'held to account' via the BBC, Twitter, etc. It is for institutions themselves to stop being performative parodies of themselves - sending themselves out as avatars in the pretendy world of media narratives - and go back to the boring work of doing their work properly in accordance with technical standards of adequacy.
I don't mean they shouldn't be subject to appropriate, informed scrutiny by specialist journalists such as the TES journo that Arday tried to shut down. I mean that the frisson of coverage generated over the last couple of weeks is a pantomime - the same as the pantomime that Cambridge laid on by appointing someone with the objective of acquiring a poster boy rather than a seasoned intellectual expert.
The pantomime is laid on for us - the overly online consumers of facile narratives. If we all stepped back a bit from our virtue-signalling consumption and embellishment of these narratives then perhaps institutions, too, would get better at becoming themselves again, instead of making hollow performances.