I think what is meant is that your analysis of people is different when they say the "right" things. The wife-murdering Earth Day founder comes to mind.
As Dag Hammarsköld said: It is much more difficult to care about those close to you than those far away.
I have seen plenty of people that use implicit accusations as a means of getting ahead. White, "angry", old men is a term that's been popular lately - I will use that as an example.
Are all old, white men "angry"? Are only the old, white men that disagree with the speaker "angry"? Are old, white men angrier than old men in general? Than old, white women? Than <colour> [menopausal|child-caring|single] women? Is there some skew in who brings their opinions to market? In who is heard?
I say that the people that the most seductively claim some one is biased, are those most likely to sweep their own biases under the rug.
Furthermore, I claim it is a much better goal to be consciously fair in one's dealings, than to seek some mythical state of "biased-less-ness". It seems more work, but it truly brings greater rewards to you and the people you deal with.
Trying to be "unbiased" leads to exactly zero good, because it isn't how the human mind functions. I will put my own family before the stranger on the street. That doesn't mean I won't help the stranger on the street that I _see_ needs it. I need a functioning mind for that, and this college nonsense about bias is something I had to unlearn to do so, as it leads to cowardice at the hint of personal danger or embarrassment.
(Unless, of course, you dont't perceive a real threat, but just some poor sod you can lecture about how morally superior you are.)
[EDIT: Spelling]