In the dynamics of atoms and molecules at metal surfaces, electron-hole pair excitations can play a crucial role. In the case of hyperthermal hydrogen atom scattering, they lead to nonadiabatic energy loss and highly inelastic scattering. Molecular dynamics with electronic friction simulation results, based on an isotropic homogeneous electron gas approximation, have previously aligned well with measured kinetic energy loss distributions, indicating that this level of theoretical description is sufficient to describe nonadiabatic effects during scattering. In this study, we demonstrate that friction derived from density functional theory linear response calculations can also describe the experimental energy loss distributions, although agreement is slightly worse than for the simpler isotropic homogeneous electron gas approximation. We show that the apparent agreement of the homogeneous electron gas approximation with experiment arises from a fortuitous cancellation of errors as friction is overestimated close to the surface and the spin transition is neglected. Differences in frictional treatment affect single, double, and multibounce scattering trajectories in distinct ways, altering the shape of low-temperature energy loss distributions. These distinctions are largely absent at room temperature but may be measurable in future low-temperature scattering experiments.