We consider the vibronic properties of molecular Rydberg states in the strong coupling (degenerate) limit of the ion core, and show how the observed optical Rydberg spectrum for such a molecule is closely related to the Franck–Condon spectrum of its Jahn–Teller ion core, regardless of the symmetry labels attached to the Rydberg electronic species. These relationships permit the resolution of a quarter-century old paradox in the Rydberg spectrum of benzene and give rise to easily verifiable predictions concerning benzene’s vibronic spectrum, which are applied to a recently discovered new Rydberg series. We further suggest that observed deviations from the idealized Rydberg case discussed here will reveal additional details about the coupling of Rydberg electronic and core-vibronic motion.