In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network.