With all due respect, you don't seem to understand what I am saying: I completely agree that such measurements will show that space is curved, it's not like we disagree there. These measurements are however appearances, with the twist that such measurements provide the only viable map of locations.

The real space is useless for most intents and purposes (since our interactions are bounded by the properties of light and gravity, and thus appearances is what guides us).

It seems important to make the conceptual distinction however, and not confuse reality with appearances, in this case as well as every other.