The government can't keep their own secrets contained most of the time. They are not controlling the media. That is beyond silly to even suggest.
No, that comparison doesn't come up literally ever that I've heard from. I do recall several anti-war pieces in NY Times and others encouraging us to not back Ukraine, the usual war hawk pieces suggesting to escalate, and a bunch of poorly written stories that rehashed weeks old tweets.
As the joke goes there are two kinds of people: those who believe in conspiracies and those who have actually interacted with the government.
The closest you might get is something like Journolist which was Ezra Klein trying to convince other news heads to parrot his takes - which is a disgrace, but not some secret conspiracy.