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 $λ_B$ and all users form another independent PPP of intensity $λ_U$. 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 $\exp(-\frac{λ_U}{λ_B})$ 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.