I'm very sympathetic to Greene's views. In fact, I'm mid way through a philosophy PhD on evolution and morality myself (more at http://ockhamsbeard.wordpress.com/). However, I'd never read Greene's entire dissertation - so thanks for the link.
On his views, there's one point I'd like to raise. The reason why "people tend to believe that moral judgments are produced by reasoning even though this is not the case" goes back to the evolutionary roots of our moral intuitions.
Assuming that morality has evolved to encourage pro-social behaviour, it’s pla...
Group seleciton indeed. Although I'm talking about both biological and cultural evolution working together, and in such a context, group selection is plausible (not that it's entirely implausible in biological evolution).
See Haidt & Kesebir (2009) for an overview of group selection in this context.
In short, it's not all about altruism but about group cohesion, and promoting group cohesion doesn't need to come at the same cost that accompanies altruism.