I'd say "nicely done, edsheppa," except you neglect to account for one pesky detail: innate human values. From whence do these arise?
Yes, I've been conspicuously silent about that, haven't I? The reason is that, for the purposes of my argument, it is not material. Whatever the source of these values, the argument stands.
However, since you ask, I will tell you my opinion. First, they are biological, a product of our brains and bodies. Feeling that you've been treated unfairly or feeling sympathy for someone else so treated come from within us just like feelings of hunger.
Second, we don't have a detailed understanding of how these feelings actually work inside us but I consider it probable that, in time, we will.
Third, and I'm sure you expected this, I think it's probable that our capacity for these innate feelings and for the ability to wrap rationality and culture around them to improve our well being is an evolutionary endowment. Again we aren't even close to understanding the details of how that could have happened but, in time, I think we will. In broad strokes though the story will be that groups with innate moral leanings and capacity are more fit than those without.