A nuclear reactor system is a very delicately balanced system for sustained chain reaction controlled by the control rods.
As in fukushima reactors, which are light water reactor where you have enriched uranium, the criticality depends heavily on the core configuration and the position of control rods.
In a core meltdown, what it meant is the uranium core get melted and settles down and the core configuration gets damaged; for control rod mechanism to work the control rods should be surrounded by active core
Actually, that's how reactor power is reduced by inserting the control rods into the core, Now, when core meltdown occurs the core becomes inaccessible for control rods, since it settles down.
So, the question whether control rods melts is heavily dependent on the mature of accident. Control rods are generally made of stainless steel with boron or cadmium or hafnium, while core is Uranium which is somewhat like soft metals sodium having melting point near 1100 degree Celsius, while SS has melting point near 1500 degree Celsius. Again some reactor used $UO_2$ as fuel which has higher melting point than metallic uranium. I don't know fukushima used which one!!
So, due to the temperature difference, is seems unlikely that control rods melted in fukushima, rather it seems to me that control rod melting is a good thing for controlling the reactor in case of a core meltdown.