This paper considers the study of cooperative manipulation of a cable-suspended load with two aerial robots and without explicit communication. The role of the internal force for the asymptotic stability of the beam-position/beam-attitude equilibria is analyzed in depth. Using a nonlinear Lyapunov-based approach, we prove that if a non-zero internal force is chosen then asymptotic stabilization of any desired beam-pose configuration 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. Non-zero internal force can be interpreted then as a fundamental factor that enables the use of cables as implicit communication means between the two aerial vehicles in replacement of the explicit ones. Furthermore, the formal proof of the system output-strictly passivity with respect to an energy-like storage function and a certain input-output pair is given. This proves the stability and the robustness of the method even during motion. The theoretical findings are validated through numerical simulations with added noise and realistic uncertainty.