I think that both people and governments should work from both stories and statistics. Statistics help us understand one way. As narrative creatures, stories help us differently. In particular, I think empathy is much easier to find with stories than raw data, and empathy is vital for functioning societies.
As to noticing privilege, I think we have good ways to measure some sorts of privilege. E.g.:
http://www.nber.org/papers/w9873
http://www.nber.org/papers/w5903
http://www.pnas.org/content/109/41/16474
But I think it's incumbent on all of us to understand what power we have and use it wisely. For me, both stats and stories have been useful. The stats are widely available, but here are some collections of stories:
http://projectunbreakable.tumblr.com/
And I also really benefited from Project Implicit, which helped me understand how my own subconscious biases were contributing to various societal problems:
https://implicit.harvard.edu/implicit/
For me, privilege checklists have been helpful in seeing how I got lucky, what advantages I happen to have:
http://danilocampos.com/2013/02/unpacking-my-knapsack-the-pr...
http://amptoons.com/blog/files/mcintosh.html
I also really benefited from seeing these issues as the tail end of long historical imbalance. E.g.:
http://www.theatlantic.com/features/archive/2014/05/the-case...
http://www.amazon.com/Why-Does-He-That-Controlling/dp/042519...
I definitely agree with your point that spokespeople and media gatekeepers are often part of the problem. That's what makes me hopeful about things like Twitter. There I can make a decision to seek out individual voices and add them to the mix of what I see every day.
Is that helpful?