Nobody is privileged in absolute terms. Everybody has their own troubles. Groups (racial, social, whatever) are a useful abstraction, not a reality. And if anyone has to compensate anybody for anything, that's what the justice system is for.
The justice system is ideally intended to provide fair and impartial justice, but I think it's also fair and reasonable to point out when it falls short of that ideal. In fact, in a democratic society, I would argue that an informed and vocal public is a necessary component of keeping institutions accountable to the people.