This paper proposes a direct data-driven approach to address decentralized control problems in network systems, i.e., systems formed by the interconnection of multiple subsystems, or agents. Differently from previous work, in this paper we assume that coordination among agents is limited in the data collection phase. Specifically, while we allow for multiple experiments to be performed on the network, these can be asynchronous (meaning that we do not require that all agents take part to each experiment). We focus this study on an open-loop optimal control problem, and propose a strategy to reconstruct the missing experimental data, i.e., data from the agents not participating to a given experiment. Importantly, our data-reconstruction strategy does not compromise the performance or numerical reliability of the approach, as we give conditions under which the missing data can be exactly reconstructed. We complement our findings with numerical simulations, showcasing the effectiveness of our approach in decentralized control scenarios.