No, nor does it prove that champagne and beer are the same drink as the discussion indicates. The point is that the example uses a very limited set of attributes: you can add attributes, say "sweet" or "made from grapes" to distinguish nodes still further. Without enough distinguishing power in the attributes chosen, a particular concept analysis may be unsound: it may identify things that are not identical. So you need to prove soundness if you want to make this kind of inference based on the model.

The limit of this operation gives you something similar to Leibniz's rule, where two things are identical if the same class of (first-order observable) predicates are true of them.