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As I understand it, E. F. Codd demonstrated conclusively that any data schema can be normalized into the relational model. Thus I believe it is logically impossible to show an "example of structured data that doesn't fit the relational model but does fit the XML model".
The use case issue comes down to pragmatics, not theoretics: XML and XDBs tends to be a more *practical* solution for data that irregular, deeply hierarchical, and recursive ... like an awful lot of real world documents, or data about real-world hierarchies (organizations, component-subcomponent assemblies, etc.). One can certainly build a pure relational model of these things, and might possibly be able to build a relatively portable SQL implementation, but one hits all sorts of practical limitations - multiway joins are usually required (which gets pretty slow in practice with more than a few tables), queries get complex, and only a few geniuses can understand how it all fits togther.
XML and XML-capable DBs allow ordinary mortals who've "got XML" to work with this sort of data in a standardized, portable, and reasonably efficient way. The theoretical links back to the relational model are being forged, albeit slowly. A couple data points for that: Don Chamberlin, one of the inventors of SQL, is editor of the XQuery spec; and some of the set theory that Codd cited in his original work has been shown to handle XML (see xsp.xegesis.org for a collection of papers).
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