So should the physics and chemistry teachers at our school, but they disagree. Somebody's gonna have to eat crow. Given that, however, I will assume that your 'hot' water is higher in temperature than your 'cold' water. I would like to hear both sides of the opinions of your faculty. The reason is that the surface of the freezer usually has a layer of ice on it.
Ice is an excellent insulator, and therefore limits the heat transfer to the freezing surface.
That book is the first place to look for answers to questions of the type that you posed. Jack L. Uretsky, You will recall that the question was does hot water freeze faster than cold water. I don't recall it mentioning a freezer, nor a coating of ice, nor allowing for escape of some of the targeted hot water to freeze. I maintain my answer as correct, given the question that was asked. Naturally if heat is allowed to escape from the system, either thru melting of a supposed coating of ice or warming of some freezer space, than your assertion might change the scenario.