Aren't current explanations for the evolution of human cooperation a little too reductionist?
Interesting question! 

I think that in terms of 'tribal' fitness, altruism would be strongly selected for, as communities would tend to be quite small (relative to, say, a town today). In modern civilization cultures have developed differing levels of altruism, but I imagine this is a result of upbringing rather than inherent differences in tendency toward altruistic actions.

So in my opinion you cannot rule out altruism being selected for because it is clearly an advantage (in terms of survival / fitness) in smaller communities - we just don't live in that kind of society any more; people don't have to be altruistic to get by, and this kind of mind-set can 'evolve' culturally, outside genetics. But on the whole I would still argue that most people are inclined toward altruism - ether because they feel naturally inclined to help others, or feel that by helping others some benefit (such a reputation) would be bestowed upon them (the former may be the same as the latter, but at an unconscious level).