The liberal media bias goes back to the 1950's... Alan Drury's "Advice and Consent" (the liberal spin-meister in that novel was a guy named "Frankly Unctuous" and he was a dead-ringer for the liberal nightly news guy: maybe David Brinkley before he turned somewhat conservative at the very end of his career) was a good example back then. The way the media ganged up on Barry Goldwater and the other "influentials" followed: remember the National Association of Psychologists (or whatever it was called) who declared Barry "unfit" to be President? And after Vietnam and Watergate, the floodgates opened.
Conservatives started getting their act together in the late 70's and early 80's with the early think-tanks (Heritage, Cato) that started stepping up and challenging the conventional "wisdom" -- and Reagan crushed the liberal media despite their best efforts.
Guys like Parry can harrangue all they want, they can't dodge the facts and reality... But there are too many alternatives now and the liberal media will never have the kind of influence it enjoyed in the past, especially allowing the crimes of the Clinton era to pass with hardly a wimper (despite the alleged "tough coverage" Bubba received). A Republican in that situation would have been hanged.