© 2016 American Physical Society. The distribution of single-particle strength in Ni67,69 was characterized with one-neutron knockout reactions from intermediate-energy Ni68,70 secondary beams, selectively populating neutron-hole configurations at N=39 and 41, respectively. The spectroscopic strengths deduced from the measured partial cross sections to the individual final states, as tagged by their γ-ray decays, are used to identify and quantify neutron configurations in the wave functions. While Ni69 compares well with shell-model predictions, the results for Ni67 challenge the validity of current effective shell-model Hamiltonians by revealing discrepancies that cannot be explained so far. These results suggest that our understanding of the low-lying states in the neutron-rich, semimagic Ni isotopes may be incomplete and requires further investigation on both the experimental and theoretical sides.