Recently, several authors have reported specific criteria to support the widely accepted use of a convex operational model for bulk energy storage in the formulation of power system operation and planning problems involving binary variables. Using two counterexamples, we show that this modeling simplification may give rise to impractical solutions featuring simultaneous charging and discharging, even though the recently published criteria are satisfied. Thus, both counterexamples invalidate those criteria and demonstrate that the customarily used convex model may be unsuitable for the precise incorporation of bulk storage in such instances of mixed-integer programming.