How do you propose to measure the ultralocal Riemann curvature? I agree with you that it can be there in an exact solution, but I don't really agree that it's necessarily physical (there are many many exact solutions which aren't, for starters). Even with a broader definition of local, a Synge 5-point like process is not going to find a failure of parallel transport in a sufficiently small region. Would you be satisfied with "effectively flat" (in an EFT sense) or even "FAPP flat"?