My response to this situation is to say that proof theory is more fundamental and interesting than model theory, and pragmatic questions (which the dialog attempted to ask) are more important than model-theoretic questions. However, to some extent, the problem is to reduce model-theoretic talk to more pragmatic talk. So it isn't surprising to see model-theoretic talk in the post (although I did feel that the discussion was wandering from the point when it got too much into models).