I think that the problem here is that it seems self evident to Mourn (and dare I say, most of us) that the two are not logically identical, therefore we're having a hard time wrapping our heads around your contention that they are.
I use computational and mathematical models in my work. The definition of a model is, "a simplified representation of reality". Because they are simplified, the model is never exactly the same as reality. There will always be cases where the model is inconsistent with the real world. When using a model, you have to be aware of when and how it might be inconsistent with the real world and make sure that those inconsistencies won't affect your results (or at least acknowledge that effect when you report those results).
A set of role-playing game rules is a model. In this case, since D&D is a fantasy game, it is a representation of an imaginary reality, rather than the real world. While this reality exists only in the minds of the players and the DM, the RPG rules still share the other characteristics of a model, including simplification. Because it is a simplification, it can never be entirely consistent with the imaginary world that it is modeling. Therefore, the rules of the game are not the physics of the game world. There will be cases where the game rules are inconsistent with the imaginary world that the players and the DM are creating, like the Bag of Rats. Much like the scientist who has to recognize and deal with inconsistencies between the model and real life, the DM has to recognize and deal with inconsistencies between the rules and the imaginary world that he and the players are creating. This is one of the major purposes of Rule 0.