The zero-phonon line (ZPL) and the sideband in the vibronic spectrum of a single glyoxal molecule inside a He-3 droplet are analyzed within the framework of the Lax formalism. The new theory takes full account of the coupling of the molecule to the single particle-hole (PH) and collective excitations of the doped Fermionic droplet. The effect on the coupling of the wavevector dependence of the effective He-3 mass and the large local density of the first He-3 shell, resulting from the interaction with the chromophore, are also included in the theory. By fitting of a coupling parameter and the phase factor between the PH and collective response functions, the shape and relative intensity of the observed ZPL and its slowly decreasing multiexcitation sideband are well-reproduced. The new theory is consistent with the previous explanation of the surprisingly sharp phonon line superimposed on the sideband in terms of the dense first He-3 shell, which acts as a Helmholtz resonator for the zero sound of the droplet.