You know, one could be forgiven for thinking you don't read even your own posts. I quote you
Answer me this: If a valid non-metric theory of gravitation exists, why is there any need to "understand the physical reality of the metric"?
When I disagreed to the extent that even I understood the metric, you responded with link that pointed that there is at least one non-metrical theory of gravitation. And this is not Einstein's, which you refer to aboveEinstein general relativity is a metric theory, what is the physical reality of metric, none knows.
Answer me this: If a valid non-metric theory of gravitation exists, why is there any need to "understand the physical reality of the metric"?