The effective spin-mixing conductance (Geff↑↓) of a heavy-metal-ferromagnet (HM-FM) interface characterizes the efficiency of the interfacial spin transport. Accurately determining Geff↑↓ is critical to the quantitative understanding of measurements of direct and inverse spin Hall effects. Geff↑↓ is typically ascertained from the inverse dependence of magnetic damping on the FM thickness under the assumption that spin pumping is the dominant mechanism affecting this dependence. We report that this assumption fails badly in many in-plane magnetized prototypical HM-FM systems in the nanometer-scale thickness regime. Instead, the majority of the damping is from two-magnon scattering at the FM interface, while spin-memory-loss scattering at the interface can also be significant. If these two effects are neglected, the results will be an unphysical "giant" apparent Geff↑↓ and hence considerable underestimation of both the spin Hall ratio and the spin Hall conductivity in inverse or direct spin Hall experiments. © 2019 American Physical Society.