Well, truth exists—the average member of "the right" surely does not deny that.
If "unbiased reporting" simply entails a good-faith effort to provide the public with accurate and relevant information, without taking its political implications into account, then it is a perfectly coherent concept. Yet herein lies the problem: A good reporter publishes those things that are both accurate and relevant. But accuracy and relevance can only be determined through the use of human judgment.
What is important is to regularly expose yourself to the arguments of those you disagree with. I am not a fan of John Stuart Mill, but even a broken clock is right twice a day, and this passage is dead-on (emphasis mine):