Guessing by how this word is typically used, it means: "My opponents are cognitively inferior. They can't understand my situation, because they have never experienced it. On the other hand, I can perfectly understand their situation (despite never experiencing it, too)."
I don't think it's implausible to believe that people pay more attention to those who have higher status than themselves, and less attention to those who have lower status. Furthermore, I believe in the snafu principle (people don't give accurate information if they'll be punished for it*).
Unfortunately, the true parts of the idea of privilege are apt to get swamped by the way it's used as a power grab.
*The original version framed this as an absolute. I'm quite willing to be probabilistic about it.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Of course, for "every Monday", the last one should have been dated July 22-28. *cough*