I have a lot of trouble with arguments like this as well. I think surface forms are just that-- realizations of underlying configurations, without any particular limits on what surface forms can be produced. So establishing things like modification and argument structure is deeper, but after that it's just working out how the various pieces fall together, not some mysterious underlying genitive.
This book also seems to take on a have-your-cake-and-eat-it-too position of order in non-processing Generativism. It starts off as X and then becomes Y, yet this is saying NOTHING about how it's actually processed in the mind. That is therefore completely irrelevant and just a big metaphor, not actually giving us any more information than the descriptive generalizations in the first place. If this was supported by psycholinguistic experiments, that would be cool. But these theories are specifically/intentionally not about performance, just competence, so even if they happen to be right, they are not as theories making predictions about order at all. That always puzzles me.
(For the record, my objections are to the methodology/assumptions, not the conclusions in particular. There's no reason I'd assume that nominative [or any case in particular] is the obvious default in any one language or in all languages.)
