If you read the actual research article, it's pretty clear. They had two control cows - one that was left alone, and another painted all one color (black) using the same paint as the stripes. There was no difference between black paint and no paint, only striped paint.
It's a visual problem. Flies can't resolved the striped area as a solid surface, and so do not try to land on it, they either avoid it, or crash w/o biting. They mention several other studies on this phenomenon, like that a rotating drum of striped colors attracts fewer flies than a solid one.