This is a misunderstanding of what a melt-down is. In every case we know of involving commercial reactors, fuel melt-down happened when the reactor was non-critical, completely devoid of fission.
Meltdown happens when the heat generated by decay of products produced when the reactor was critical cannot be removed fast enough, such as when a cooling system fails or coolant does not cover the fuel modules.
Any reactor with solid fuel and a high enough energy density will have a meltdown possibility, unless it is somehow using a reaction chain that precludes the production of high-activity fission products.