Despite the supposed simplicity of double-closed shell nuclei, conventional coupled-channels calculations, that include all of the known collective states of the target and projectile, give a poor fit to the fusion cross section for the 16O + 208Pb system. The discrepancies are highlighted through the experimental barrier distribution and logarithmic derivative, that are both well defined by the precise experimental fusion data available. In order to broaden our search for possible causes for this anomaly, we revisit this system and include in our calculations a large number of noncollective states of the target, whose spin, parity, excitation energy, and deformation parameter are known from high-precision proton inelastic-scattering measurements. Although the new coupled-channels calculations modify the barrier distribution, the disagreement with experiment remains both for fusion and for quasi-elastic (QE) scattering. We find that the Q-value distributions for large-angle QE scattering become rapidly more important as the incident energy increases, reflecting the trend of the experimental data. The mass-number dependence of the noncollective excitations is discussed.