I've read the first couple of pages and the first thing I'm noticing is that the author is taking categorisations and boundaries that humans have defined (e.g. "families" and "solar systems") as evidence that hierarchy exists in nature. I find this to be really unconvincing. All it shows is that we're evolutionarily designed to cluster "similar" (spatio-temporally co-located or semantically similar) entities and give them names. That much I agree with. But that's not an argument for organising systems into strict hierarchies! It suggests we should group entities together (conceptualise them) whenever there are intuitive ways to do so.

I'd say the only true thing about natural organisation is that it operates by proximity, and we humans take that proximity and stratify it.