Joint-stability in interindustry modeling relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots, offering a mathematical demonstration that shows the impossibility of mutual consistency between demand-driven and supply-driven models. Mutual consistency would entail that coefficient matrices under both model versions would remain constant when the economic equilibrium changes following an external shock.