To validate this hypothesis, we conduct a control study in this work. Specifically, we compare the results obtained from a mixed quantum-classical simulation with those from fully quantum-mechanical simulations. In the mixed quantumclassical approach, the cavity radiation mode is treated classically via mean-field forces, whereas all other degrees of freedom are treated quantum mechanically using the hierarchical equations of motion (HEOM) approach (see Ref. 53 and the literature therein). We find that extracting rates directly from the slope of the population dynamics can lead to spurious resonance peaks which disappear when calculating the rate using the rigorous flux-correlation function formalism. Therefore, when implemented correctly, the mixed quantumclassical method does not recover the quantum-mechanical results, which thus confirms the critical role of the quantum nature of the cavity radiation field in the study of cavityinduced chemical reactions in the electronic ground state.