In a recent paper, network management rules were evolved to maximize sum throughput of two co-existing underlay secondary networks that reuse the spectrum of a licensed primary network. Such rules require secondary networks to either transmit concurrently by optimal apportioning of the interference temperature limit (ITL), or in isolation. In this paper, we analyze the secrecy outage performance of the primary downlink network for a scenario when receivers of the two co-existing secondary networks are untrusted and eavesdrop on the primary downlink transmissions. We analytically establish that it is only when secondary networks transmit concurrently, that the primary network is most secure. Further, we derive an optimum ITL apportioning mechanism that guarantees maximum secrecy for the primary network, and also present closed-form expressions in a special case. The optimum apportioning parameter shows that the network management rule that maximizes secrecy of the primary network is not the same as that which maximizes secondary sum throughput. Computer simulations are presented that demonstrate accuracy of the derived expressions.