  Cosmologies that match in a volume averaged sense need not generally have the
same light propagation behaviors. In particular a universe with inhomogeneity
may not demonstrate the Friedmann-Robertson-Walker distance-redshift relation
even after volume averaging to FRW spacetime. Even the Dyer-Roeder prescription
for incorporating inhomogeneity within a universe equivalent to FRW in an angle
averaged sense does not guarantee FRW behavior in general. To legitimately use
the FRW distance-redshift relation to interpret observations, the physical
conditions must match in a line of sight sense (defined herein: most
observations do), since light probes the mass distribution or geometry on all
length scales.
