For many decades the lead chalcogenides PbTe, PbSe, and PbS (and their solid solutions) have been preferred high-performance thermoelectric materials due to their exceptional electronic and thermal properties as well as great stability during operation. However, there is a lack of understanding about the fundamental relation between the reported high-defect crystal structure containing cation disorder and vacancies and the observed transport properties, which follow expectations for an ideal rock salt crystal structure. Here we have studied a series of undoped lead sulfide samples (Pb1-xS) with presumed small chemical variations. Crystallographic refinements of high-resolution synchrotron powder X-ray diffraction data give unphysically low lead occupancies (0.75-0.98), in contradiction with the measured charge carrier concentration, resistivity, mobility, and Seebeck coefficient, which show no signs of lead vacancies. A new Rietveld refinement model including preferred orientation parameters and anisotropic strain gives almost full lead occupancy and improved agreement factors. However, transmission electron microscopy analysis reveals that there is no preferred orientation in this system. Instead it is the diffuse scattering due to directional correlated disorder in the structure that necessitates the additional parameters when modeling Bragg intensities. The present approach is a general method for absorbing effects of direction-dependent correlations in advanced materials.