Conducting data analysis and system monitoring in a privacy-preserving manner is extremely important for anonymity systems such as the distributed publication system Freenet. The current obfuscation mechanisms for gathering statistics in Freenet are designed to anonymize both the responding node and the response itself. We show that due to the possibility of repeated targeted queries, hidden information, which can be potentially abused to damage both individual users and the system as a whole, about specific nodes can be derived using Bayesian Statistics. Our evaluation, using both an in-depth simulation study and real-world measurements, show that the hidden information can be inferred accurately in more than 86% of all experiments, with a relative error below 0.05 in more than 99.5% of all considered scenarios. Furthermore, we present an initial design for an improved obfuscation method, which is guaranteed to provide k-anonymity.