As I read scientist-philosophers such as Dawkins and Gould, and I think Shubin, they argue that the self-consistent universe described by natural science also encompasses human culture, and therefore that laws of the evolution of life apply to human culture. For example, Shubin cites as a law that every organism has parental stock. This may seem a no-brainer, but on it zoology has built a remarkable picture of the evolution of life.
Of course people are free to behave in ways not strongly determined by science, but this does not mean our behaviour is not caused, or that we inhabit a 'nature' that is somehow separate from material nature. This issue is at the root of the dispute between science and religion, in that religion claims access to a miraculous 'special revelation' whereby human life is somehow separated from the context of natural science, while science says that consistency means all culture obeys the laws of science. So I do think scientists claim that when they categorise nature, human culture has its place within the overall scheme, described by taxonomy, phylogeny and more specific empirical methods. As I see it, recognising this natural context of culture is a key to overcoming the alienation of humanity from nature, and also of understanding such mythic narratives as the fall from grace.
I don't think the unity of nature is just a gleam. At the religious level it goes back to the old Hindu idea that all is one. For science it reflects the assumption that the laws of physics apply consistently, and the goal of a theory of everything, integrating the four forces of physics in the Standard Model - http://en.wikipedia.org/wiki/Standard_Model
Shubin is showing us the unity of nature in the most beautiful way we can imagine - that all our innards are largely shared with the tree of life. DNA on earth has a unity which science is now unpacking in all its marvelous elegance. It would be completely inelegant to say there is an aspect of life, namely culture, which is not part of the tree of life.
DWill, you seem to be implying that culture is a superstructure without causal basis in nature. Karl Marx had interesting views on this. I agree with this base-superstructure distinction to some extent, except that nature provides our bearings, speaking of collective humanity rather than at the individual level. When we are attuned to nature, we can steer a course through its hazards, but when we lose contact with nature we are like a ship drifting onto rocks.
The core message which I take from Your Inner Fish is that we can learn from the history of life about the real challenges of evolution, and help humanity to understand its real place within the river of time, learning from our origins in the distant past to help understand our present situation and choose our possible future destinations.