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It's true that there are plenty of people who understand the core government-amplifying function of the establishment media, but there are also plenty of people -- likely far more -- who don't.
I want to explore the ugly double-standard that you seem to have exposed. Even if, according to Collins, it is generally assumed that "military analysists" are biased in favor of the Pentagon, it is at least as true, as you say, that, "The public has long been inculcated with the notion that we have a "liberal media" that opposes and undermines whatever Republicans do, etc. etc."
However, note that when press behavior emerges that supposedly confirms the "liberal media" theme, that instance of behavior itself becomes enormous news, sometimes even consuming a week's worth of news cycles. This was the case when the NYT wrote its unflattering article about McCain and the female lobbyist, if you recall, when almost the entire establishment media closed ranks around McCain to condemn the Times' "bias."
Yet, at the same time, when a story comes out exposing - in lurid, undeniable detail - the converse "military favorability" theme, the story is entirely written off as something everyone already knew.
You can play this game with countless examples, where each and every example of "liberal media bias" is relentlessly spotlighted and commented upon, while examples of military/hawk favoritism go ignored - even though both themes are supposedly common knowledge.