The specific situation that is burned in my mind was a black girl who was in a math PhD program at the same time that I was. The department wound up bending their rules to the breaking point to give her a Masters on her way out because nobody wanted to risk the discrimination lawsuit that she was threatening. Her actual math knowledge was not even to the level that I would expect from a BSc in math.
I have never witnessed anything involving a white person that was anywhere near being similarly egregious. And I had experiences with that department which demonstrated in spades that white people were not given anywhere near as much leniency.
As for your final point, I thought I pretty much said that. I've not seen the specific studies that you're referring to.