If I remember correctly, they weren't sure. The proposed mechanism was indeed (again, if I'm remembering correctly) that it's antioxidant properties combated the excess oxidizing agents and mechanisms caused by radiation exposure. It helped mostly with soreness of joints, being only a quality of life kind of finding, and didn't have an effect on the radiation treatments success rates.
Now let's see if I can find that paper and how close I was.
EDIT:
Well that was easy to find. Smallish study, looks like I was basically correct. Seems to have helped with inflammation related issues. Hydroperoxide levels were lowered by consumption of the water, so that mechanism looks very plausible within the bounds of information the study provides.