That's true, I heard that water has more radiation than anything.
Deuterium, or heavy water, which is H30, is highly radioactive, however H20 itself can only become contaminated if the minerals in the water become contaminzed - generally unless it is highly mineral rich with minerals that give off active radioisotopes such as radioactive materials then there is no radiation in it. If the water was 100% pure, with no garbage, minerals, or other contamination you could take a dip in a spend fuel rod containment pool.
In fact pure water is a radiation inhibitor and it is why they use it in nuclear reactor storage containment - it acts as a shield by slowing the highly excited electrons that would otherwise travel as far as they could. I have a picture of newly spent fuel rods from a Canadian CANDU reactor...they literally glow this beautiful bluish-purple until they "cool" radioactively for about a month or so. The glow is caused because the flow of electrons is so intense that they literally rub together so fast and so hot they create photons.
Water is perfectly safe, and gives off no real radiation of any sort, or shouldn't. It's the mineral's in the water that are the real culprits - they are directly radioactive, or can become contaminated.
P.S. I worked at a nuclear power plant doing contract work for the Canadian government in nuclear security.