The Selfish Gene - a twist in our tail ?

In 2007, Felix Warneken and colleagues from the Max Planck Institute for Evolutionary Anthropology found compelling evidence that chimps behave altruistically in a very human way. They help out unrelated strangers without expectation of reward, and even go to great lengths to do so. Most humans, the vast majority of them, do not.
Just why are humans so selfish ? If a community or a nation is selfish this can be explained by getting a couple of anthropologists or historians, as well as psychologists into a huddle and thereby, a coherent conclusion, if a Corporation is selfish, it can be explained away by saying that so-and-so owns 83% of it and he is selfish, so, well, the Corporation is selfish. But all (or substantially all) of humanity ?
While we are forced to conclude that the streak of selfishness exists amongst humans at a gene level (else it simply couldn't be this universal), what strikes me as remarkable is that the animal life that comes closest to humans are utterly selfless amongst their own. Three examples of gregarious species with big brains (and bigger hearts) are chimps, elephants and dolphins. Its astonishing that we have evolved (allegedly) from them, and have left the quality of selflessness behind. I read a true story the other day, of a man who would have drowned in the Atlantic Ocean, but for a couple of dolphins who actually took him on their backs close to shore. Would the human ever do this service to a predator ?
And take the chimp. We - you and I - are 97% chimpanzee. We inherited some of its bad qualities, male chauvinism being a resplendent example, and ignored its selfless nature. My question is, just how did selfishness find its way into the other 3% of our gene pool ?