In the angle-averaged excitation and decay spectra of molecules, vibronic coupling may induce the usually weak dipole-forbidden transitions by the excitation intensity borrowing mechanism. The present complementary theoretical and experimental study of the resonant Auger decay of core-to-Rydberg excited CH4 and Ne demonstrates that vibronic coupling plays a decisive role in the formation of the angleresolved spectra by additionally involving the decay rate borrowing mechanism. Thereby, we propose that the angle-resolved Auger spectroscopy can in general provide very insightful information on the strength of the vibronic coupling.