Lately, the problem of cell formation (CF) has gained a lot of attention in the industrial engineering literature. Since it was formulated (more than 50 years ago), the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods (including those for a popular model based on the p-median problem, PMP) are prone to two major types of errors. The first error (the modeling one) occurs when the intended objective function of the CF (as a rule, verbally formulated) is substituted by the objective function of the PMP. The second error (the algorithmic one) occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches.