The problem with those "studies and surveys" is that they rarely, if ever, properly define "main stream news media."
Is, say, conservative talk radio "main stream news media"? The average person would probably say "no, it's opinion"; however, a great many of the millions upon millions who listen to Rush will take what he claims as gospel. When opinion and information have been so cavalierly mixed, pretty much anything could be construed as "news media."
Now, could it be said that most "main stream news media" has a pro-government slant? Absolutely. Specifically, slanted toward those in power or those about to be. Witness the "main stream news media" beating the war drums in 2003 leading up to Iraq. Even liberal MSNBC fired Phil Donahue for speaking out against the war.
The other issue with these "studies and surveys" is that they rarely, if ever, define exactly what "liberal bias" entails. If there is a "liberal" politician and a "conservative" politician debating an issue, and the "liberal" is clearly correct on the issue, and coverage is more favorable to that, is that "liberal bias"? Or is that simply the media reporting what the facts are? Too many people see facts reported they don't agree with, since in today's hyper-polarized society people feel they are perfectly entitled to facts that support their predetermined worldview, and attribute the lack of self-affirmation to "bias."