Favorable characteristics of wireless channels (including the inherent broadcast and superposition nature) provide a fertile ground for the extension of conventional network coding (NC) principles to wireless communication networks. However, the research of emerging <bold>wireless (physical layer) network coding</bold> (WNC) techniques have already revealed several non-trivial research problems that do not appear in the conventional (wireline) NC systems, including the sensitivity to channel parametrization and challenging multi-source transmission synchronization. In this paper, we uncover another significant research challenge typical for multi-node WNC systems. We show that the performance of contemporary WNC <bold>bi-directional relaying strategies</bold> is dominated by the availability of a specific <bold>hierarchical side information</bold> (HSI), required for the successful decoding of desired information from <bold>hierarchical</bold> (WNC-coded) data streams. We analyze the impact of <bold>unreliable transmission of HSI</bold> on the performance of a <bold>wireless butterfly network</bold> (WBN), and we show that all state-of-the-art relaying strategies must be appropriately modified to avoid the deterioration of WBN performance in the <bold>limited HSI regime</bold>.