Chernobyl food contamination was mostly Cs-137 which emits Gamma rays. But Gamma rays aren't the type of radiation well suited to flip bits. To reliably flip bits, the cows would have to contain so much Cs-137 that they'd die within a day or so.

Story is likely made up.

(I could believe that a very sick cow could possibly be a significant alpha emitter after being exposed to Chernobyl... but an alpha-emitting cow isn't going to screw up a computer inside a building).