First, nobody really cares about the news wing of Fox News. Anyone can read a 3-graf bit about a car bombing in Mosul or a new ambassador to Sri Lanka. So, why are you even discussing it?
What everyone sees at Fox News is the commentators, the opinion sections. And they see that their version of "fair and balanced" (equal time for both sides) is not the same as Fox News's version of "fair and balanced" (a conservative counterweight to what they perceive as a generally more liberal media.)
Go read the things Pat Buchanan, Glenn Beck, Bill O'Reilly, Andrew Napolitano, Ann Coulter, Susan Estrich, Judith Miller, Grover Norquist, et al write in the Opinion section of Fox News's websites. Now try to find even a semblance of a liberal equivalent to that there.
Fox News has tried to take this weird high road of saying their station itself is "fair and balanced", when clearly what they meant when they kicked it off was "we are balancing ourselves against Meet The Press and MSNBC and the New York Times, etc." Which is a perfectly legitimate position.
The problem is I think they've bastardized it terribly by becoming a mouthpiece for the Republican Party even at its most wrongheaded, and I don't see nearly enough independent thinking, compromise, or moderation on their part. I don't agree with everything the Democratic Party does, and I let my Congressman (Mr. Ron Paul himself) know. But the whipping in line of a media outlet by a single party is really impressive, nobody at FOX News is ever off-message - and that's precisely the problem. There's no inner debate, not even a hint of "well, maybe we're wrong, maybe there is more than one side to this, maybe it's not black and white", and without that, I think calling Fox News "fair and balanced" is a farce.
There are plenty of liberal equivalents to this, of course, but they're just little blogs and DailyKos and The Progressive and the like. None of them are on cable TV. None of them have the weight of Rupert Murdoch and News Corp's prodigious checkbook behind them. That's why we laugh when hear what FOX News has to say. You can be biased, you can even be transparent in it, but if you're big business, don't expect people to just nod their heads uncritically.