Irrespective of how close the outcomes are to the actual facts, those two things have a different quality, don't they?
Not as much a difference as you would wish, as mean of public discourse is very actively managed, to our collective detriment, by a very small group of powerful people, which often includes the government. It's the nature of mass media, and the incestuous relationship between power and reach.
They Thought They Were Free, and all that. By the time the 'mean of public discourse' centers on something incredibly stupid or awful, nobody can be arsed to figure out who planted that idea in our heads.
In reality it's only the terminally online that seem to create these narratives.
My point isn't to pick one side or the other, but agreeing with the other poster that the LLMs are not trained specifically to parrot administration propaganda.