A comparison between theory and experiment for the benchmark H + CD4 --> HD + CD3 abstraction reaction yields a reinterpretation of the reaction mechanism and highlights the unexpected contribution of a stripping mechanism. Whereas the best analytic surface fails to reproduce experiment, a first-principles direct-dynamics (on the fly) treatment is in good agreement, showing that the H + CD4 reaction exhibits extreme sensitivity to modest differences in the potential energy surface. We find that bent H-D-C transition state geometries play an important role in the dynamics. A simple model that relates the scattering angle impact parameter and cone of acceptance accounts well for the overall reaction dynamics.