Recently [M. Xu et al., J. Chem. Phys. 139, 064309 (2013)], an unexpected selection rule was discovered for the title system, contradicting the previously held belief that inelastic neutron scattering (INS) is not subject to any selection rules. Moreover, the newly predicted forbidden transitions, which emerge only in the context of coupled H2 translation-rotation (TR) dynamics, have been confirmed experimentally. However, a simple physical understanding, e.g., based on group theory, has been heretofore lacking. This is provided in the present paper, in which we (1) derive the correct symmetry group for the H2@C60 TR Hamiltonian and eigenstates; (2) complete the INS selection rule, and show that the set of forbidden transitions is actually much larger than previously believed; and (3) evaluate previous theoretical and experimental results, in light of the new findings.