This paper studied the fundamental modeling defect existing in Poisson-distributed cellular networks in which all base stations form a homogeneous Poisson point process (PPP) of intensity λB and all users form another independent PPP of intensity λU. The modeling defect, hardly discovered in prior works, is the void cell issue that stems from the independence between the distributions of users and BSs and 'user-centric' cell association, and it could give rise to very inaccurate analytical results. We showed that the void probability of a cell under generalized random cell association is always bounded above zero and its theoretical lower bound is exp (-λU/λB) that can be achieved by large association weighting. An accurate expression of the void probability of a cell was derived and simulation results validated its correctness. We also showed that the associated BSs are essentially no longer a PPP such that modeling them as a PPP to facilitate the analysis of interference-related performance metrics may detach from reality if the BS intensity is not significantly large if compared with the user intensity.