The measured angular distributions of the elastic and one-phonon T-mode vibrational inelastic scattering of helium atoms from a low coverage (Theta(CO)=0.03) of isolated carbon monoxide molecules on Pt(111) are analyzed with a novel scattering theory. The inelastic angular distributions of the dispersionless parallel vibrational mode (T mode) are found to have similar features as the much more intense elastic angular distribution. The new theory relates the elastic angular distribution to the inelastic T-mode angular distribution, via a form factor.