This paper considers the cooperative manipulation of a cable-suspended load with two generic aerial robots without the need of explicit communication. The role of the internal force for the asymptotic stability of the beam position-and- attitude equilibria is analyzed in depth. Using a nonlinear Lyapunov-based approach, we prove that if a non-zero internal force is chosen, then the asymptotic stabilization of any desired beam attitude can be achieved with a decentralized and communication-less master-slave admittance controller. If, conversely, a zero internal force is chosen, as done in the majority of the state-of-the-art algorithms, the attitude of the beam is not controllable without communication. Furthermore, we formally prove the output-strictly passivity of the system with respect to an energy-like storage function and a certain input-output pair. This proves the stability and the robustness of the method during motion and in non-ideal conditions. The theoretical findings are validated through extensive simulations.