By combining experiments with simple model calculations, we obtain new insight in spin transport through hybrid, CoFeB/Al2O3(1.5 nm)/tris(8-hydroxyquinoline)aluminium (Alq3)/Co spin valves. We have measured the characteristic changes in the I-V behavior as well as the intrinsic loss of magnetoresistance at the onset of multiple-step tunneling. In the regime of multiple-step tunneling, under the condition of low hopping rates, spin precession in the presence of hyperfine coupling is conjectured to be the relevant source of spin relaxation. A quantitative analysis leads to the prediction of a symmetric magnetoresistance around zero magnetic field in addition to the hysteretic magnetoresistance curves, which are indeed observed in our experiments.