We revisit the thermodynamic and structural properties of fluids of homonuclear hard dumbbells in the framework provided by the reference interaction site model (RISM) theory of molecular fluids. Besides the previously investigated Percus-Yevick (PY) approximation, we test the accuracy of other closures to the RISM equations, imported from the theory of simple fluids; specifically, we study the hypernetted chain (HNC), the modified HNC (MHNC) and, less extensively, the Verlet approximations. We implement our approach for models characterized by several different elongations, up to the case of tangent diatomics, and investigate the whole fluid density range. The theoretical predictions are assessed against Monte Carlo simulations, either available from literature or newly generated by us. The HNC and PY equations of state, calculated via different routes, share on the whole the same level of accuracy. The MHNC is applied by enforcing an internal thermodynamic consistency constraint, leading to good predictions for the equation of state as the elongation of the dumbbell increases. As for the radial distribution function, the MHNC appears superior to other theories, especially for tangent diatomics in the high density limit; the PY approximation is better than the HNC and Verlet closures in the high density or elongation regime. Our structural analysis is supplemented by an accurate inversion procedure to reconstruct from Monte Carlo data and RISM the "exact" direct correlation function. In agreement with such calculations and consistent with the forecast of rigorous diagrammatic analysis, all theories predict the occurrence in the direct correlation function of a first cusp inside the dumbbell core and (with the obvious exception of the PY) of a second cusp outside; the cusps' heights are also qualitatively well reproduced by the theories, except at high densities.