Empirical correlations between characteristic H-1 NMR shifts in Pt(II) hydrides with trans ligand influence series, Pt-H distances, and Pt-195 shifts are analyzed at various levels of including relativistic effects into density-functional calculations. A dose examination of the trans ligand effects on hydride NMR shifts is shown to be dominated by spin-orbit shielding sigma(SO). A rather complete understanding of the trends has been obtained by detailed molecular orbital (MO)-by-MO and localized MO analyses of the paramagnetic and spin orbit (SO) contributions to the chemical shifts, noting that it is the perpendicular shift-tensor components that determine the trend of the H-1 hydride shifts. In contrast to previous assumptions, the change of the Pt-H distance in given complexes does not allow correlations between hydride shifts and metal hydrogen bond length to be understood. Instead,, variations in the polarization of metal 5d orbitals by the trans ligand affects the SO (and partly paramagnetic) shift contributions, as well as the Pt-H distances and the covalency of the metal hydrogen bond (quantified, e.g., by natural atomic charges and delocalization indices from quantum theory atoms-in-molecules), resulting in a reasonable correlation of these structural/electronic quantities with hydride sigma(SO) shieldings. Our analysis also shows that specific sigma(p)- and sigma(SO)- active MOs are not equally important across the entire series. This explains some outliers in the correlation for limited ranges of trans-influence ligands. Additionally, SO effects from heavy-halide ligands may further complicate trends, indicating some limitations of the simple one-parameter correlations. Strikingly, sigma-donating/pi-accepting ligands with a very strong trans influence are shown to invert the sign of the usually shielding us contribution to the 1H shifts, by a substantial reduction of the metal 5 orbital involvement in Pt-H bonding, and by involvement of metal 6p-type orbitals in the magnetic couplings, in violation of the Buckingham-Stephens "off-center ring-current" picture.