The problem I see is that you have no definition to which real object the data are tied. We agree that the problem is not the interwiki links per se. It is what results from it. How do we tie data to a wikidata page when we don't know what it is about?
This is a hard question. The best answer I can come up with now (on the bus to Oxford) is as follows: the meaning of Wikidata items is subject to social agreement, based on shared experience, communication, and human-language documentation. The latter is provided in labels and descriptions, in Wikipedia articles that are connected to a Wikidata item, and also in Wikidata property pages that document properties.
I know that this may not be a satisfactory answer to your question of how we can *really* *know* what a Wikidata item is about. If you want to dig deeper into this issue, there is a lot of interesting literature, which can give you many more details than I can. What we are dealing with is the well-known philosophical problem of /grounding/. In essence, the state of discussion boils down to the following: there is no known way of connecting the symbols of a purely symbolic system (such as a computer program) to real-world objects in a formal way. Going deeper into the discussion reveals that there is also no agreed-upon way to clarify the meaning of "real" and "object" in the first place.
In spite of all this, humans somehow manage to understand each other, which brings us to the point of how amazing they all are :-) Wikidata is but a humble technical tool that provides an environment for articulating and (I hope) improving this understanding in a novel way. This cannot provide a formal grounding, but it might come as close to this ideal as we have gotten yet.
I believe I fully agree with what you write. And I believe, we might also agree that the present Wikipedias lemmata (page) are a huge achievement towards these definitions. It is imperfect, frail, everything, but a huge achievement.
My perspective probably differs from yours only in one point: Of course it is possible to start from scratch and have a totally new community start defining the Wikidata page in a consistent, well defined manner, analysing the dimensions of misunderstanding that no single members even anticipates but which surface in a community and when working with the definitions over time. However, I think this is unlikely to happen. It is calling for the big crowdsourcing that magically appears and does the work.
My conclusions: 1. I believe it is a good feature that Wikidata allows to define concepts outside of Wikipedia. 2. I believe the Wikidate design should take more care to expressively align itself with certain, well defined Wikipedia pages, rather than requiring either of: a) a new community to redo all definitions and delimitation inside Wikidata b) require all re-users of Wikidata content inside and outside of Wikipedia to read all linked Wikipedias in all languages and understand the communality of the concept behind it. Distinguishing between closeMatch and exactMatch may do it, or alternatively a new "definingLink" relation may be called for (I am not sure which). 3. As expressed in a separate thread, I believe the links should be broader than Wikipedias, at least including Wiktionaries and Commons, but possibly much more. 4. personally I would include in the link relation role labels the concepts of narrower/broaderMatch rather than delegating this expressiveness to another part.
Thanks to all of you for this excellent discussion!
Gregor