Otherwise the paper is pointless. Fairness is still possible as long as you disregard unrelated groupings, just look at the individuals relevant traits and evaluate those so fairness isn't impossible at all. Fairness is only impossible if you want some race or group to get a certain number of spots and they wont get those with a fair distribution, in that case you made fairness impossible since you added an extra requirement, but that isn't what most people mean with fairness. The only reason to add that requirement is that you want to treat a specific group unfairly, and the most salient such group are Asians in college.
I think you should seriously take a step back and consider this from an outside point of view.
By which I mean, to a non American your obsession seems very very strange.