In this paper, the impact of network-state knowledge is studied in the context of decentralized active non-colluding eavesdropping. The main contribution is a formal proof of a paradoxical effect that might appear when increasing the available knowledge at each of the network components. Using a broadcast channel similar to the time-division downlink of a single-cell cellular system, it is shown that providing more knowledge to both the transmitter and the receivers negatively affects their performance. Eavesdroppers become more conservative in their attacks, which makes them harmless in terms of information leakage, whereas the transmitter becomes more careful and less willing to transmit, which reduces the expected secrecy capacity of this channel. Finally, it is shown that this counter-intuitive effect vanishes in the high SNR regime, in which the system becomes resilient to active attacks.