That's true, but social Darwinism is another animal, as it were. Social Darwinism isn't the same as Darwin's theory of natural selection. SD is a crude, prejudiced application of some biology to sociology; more precisely, it's a reduction of politics and morality to amoral sociobiology.

There is cooperation in nature, but social Darwinians interpret nature through the prisms of aristocracy, slavery, oppression, and so on. In any case, dominance hierarchies are real and widespread in nature too.