We compare the elastic anisotropy in hcp metals at high pressure obtained by radial diffraction measurements with those determined by other experiments and calculations. Our analysis demonstrates that in non-hydrostatically compressed hcp metals the assumption of a single uniform macroscopic stress applied to all grains in the polycrystal for the inversion of the lattice strain equations is violated due to plastic deformation. In addition, the derived apparent moduli and elastic anisotropy differ significantly from those derived from single crystals. We propose that for cobalt, rhenium and iron, the elastic anisotropy in the meridian plane is best described by a sigmoidal shape for the longitudinal velocity, with the fastest direction along the c-axis. Based on these results, we suggest that preferential alignment of the c-axis of iron crystallites along the Earth's rotation axis is the most plausible explanation for the observed P-wave travel time anomalies in the inner core.