The fungi can't break down radiation, no known method can do that(1), and probably not even collect it. The amount of radioactivity is unchanged regardless of the presence of these fungi. They only use the radiation that is there as an energy source.
(1) Bombarding with neutrons or high energy charged particles may change the amount of radioactivity. Also, positron-emitting nucleotides can have slightly faster halflife at very low temperatures. None of these methods are available for the fungi.