I think I've figured this one out. It's a result of the Humpty-Dumpty* approach to the English language in which when people begin to see that whatever you're selling is snake oil, you fix the problem by renaming the oil and adding a new list of benefits to be had from using it.
In the case of White Privilege, what they are saying is "Hey, slow down, you're making the rest of us look bad!" Back when I worked in a union shop, I'd get this from the day shift guy who resented being compared to me by the foreman. The solution to looking better than him was to slow down and make myself look worse. Right.
In the case of the WP folks, if I work hard and become successful, I need to be penalized so as to make someone else's outcome look less bad. Right.
* When I use a word, it means exactly what I want it to mean. Nothing more, nothing less. Who is to be the master, you or the word?