Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system [Abbott et al. Astrophys. J. 896, L44 (2020), 10.3847/2041-8213/ab960f]? This is the central question animating this paper. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (i) account for a 2.6 M⊙ neutron star, (ii) satisfy the original constraint on the tidal deformability of a 1.4 M⊙ neutron star, and (iii) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support supermassive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Thus, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 M⊙ compact object is likely to be the lightest black hole ever discovered.