That is until you begin to deal with an issue raised first by Thomas Kuhn in his book called the Structure of Scientific Revolutions. Kuhn argued that many "facts" build upon each other until someone begins to challenge the conventional orthodoxy. Think for a moment about living in the time of Galileo. The "facts" when he first started to deal with whether the Earth was the center or simply part of a universe - were all on one side. Using the logic of "false balance" the media of the time would simply dismiss his thinking as wrong. There should be no coverage of this wild idea that the Earth is not at the center of the universe - the science is clear. Kuhn makes the argument that ultimately progress in science, and indeed in other fields, comes from the outliers. There is already an almost natural balance on coverage for issues where there is pretty common understanding. So this extra argument for preventing false balance is unnecessary.
There are two issues where this discussion has been used frequently - Climate Change and Evolution. Both represent complex theories where a large portion of the scientific community have come down on one side of the issue. But there are enough anomalies in the data and enough alternative ways to look at the issue - that we should not accept calls to close down alternative points of view. Does that make me a Creationist? No, of course not, although many writers on evolution argue that to even express doubts about Darwin is to propose heresy. Climate Change discussion are even more unsettled. From a nonscientists perspective, a lot of the discussion seems to be based on a model which one part of the scientific community has bought into but which other parts still continue to want to raise doubts.
There is a second issue here. As often happens with the left, the idea then gets extended to issues, where while there is a preponderance of opinion or judgment on one side. As you think about the concept the sillier it becomes. The President has used this argument frequently. One column suggests that Obama "has talked about the concept of “false balance” — that reporters should not give equal weight to both sides of an argument when one side is factually incorrect. He frequently cites the coverage of health care and the stimulus package as examples, according to aides familiar with the meetings." The President is trying to dismiss legitimate criticism of policies. In the case of both the healthcare and stimulus decision - there is plenty of evidence that the alternative approaches may have yielded better results. Unfortunately, often what happens is a linkage between the yammering about "false balance" and then a demand to accept only one set of solutions (always involving more government) to solve the problem. As Bjorn Lomborg has repeatedly pointed out you can buy into ideas like the potential effect of human actions on climate without buying the lock, stock and barrel of cap and trade.
Ultimately, the argument for resisting "false balance" is a call to accept conventional logic or authority. I can understand why the left would resort to this type of discussion, but I cannot understand why so many people would fall for it.