The proliferation of mobile sensing and communication devices in the possession of the average individual generated much recent interest in social sensing applications. Significant advances were made on the problem of uncovering ground truth from observations made by participants of unknown reliability. The problem, also called fact-finding commonly arises in applications where unvetted individuals may opt in to report phenomena of interest. For example, reliability of individuals might be unknown when they can join a participatory sensing campaign simply by downloading a smartphone app. This paper extends past social sensing literature by offering a scalable approach for exploiting dependencies between observed variables to increase fact-finding accuracy. Prior work assumed that reported facts are independent, or incurred exponential complexity when dependencies were present. In contrast, this paper presents the first scalable approach for accommodating dependency graphs between observed states. The approach is tested using real-life data collected in the aftermath of hurricane Sandy on availability of gas, food, and medical supplies, as well as extensive simulations. Evaluation shows that combining expected correlation graphs (of outages) with reported observations of unknown reliability, results in a much more reliable reconstruction of ground truth from the noisy social sensing data. We also show that correlation graphs can help test hypotheses regarding underlying causes, when different hypotheses are associated with different correlation patterns. For example, an observed outage profile can be attributed to a supplier outage or to excessive local demand. The two differ in expected correlations in observed outages, enabling joint identification of both the actual outages and their underlying causes.