The Discrimination Fallacy

In public discourse you will often hear an argument of the following type; let's call it the popular logic: Group B is discriminated against, as can be seen by the fact that group B achieves less with respect to desirable outcome O than group A. Q.E.D. This is a fallacy. Why?

Another way of asking the same question is this: Which conditions would have to be fulfilled for the above argument to be sound? As far as I can see, the following suffice:

1. Members of B are as motivated as members of A to achieve a lot with respect to O, given the prerequisites for doing so.

2. Members of B are as able as members of A to achieve a lot with respect to O, given the prerequisites for doing so.

3. There are no noteworthy influences of chance that lead to a disadvantage of members of B relative to A with respect to achieving a lot with respect to O.

It seems to me that you have to first exclude possibilities 1-3 before applying the popular logic. I'm willing to typically disregard 3, as chance will tend to even out. It should also be noted that, empirically, all four influences may operate together. I am aware that such a buzzing, blooming confusion is too much for some brains to handle. It's not that four independent variables is too high a number; it's that some of these variables are owned by good people, while others are owned by bad people. They can't be at work at the same time, can they?