Water in and of itself does not become radioactive. The hydrogen and oxygen atoms cannot become fissile and unstable on their own. This water has to be contaminated with impurities from irradiated heavy metal/metalloid particles to have any detectable gamma/alpha/beta/neutron decay particles. As the water joins a larger body of water, these heavy particles separate and collect on the floor of the body of water or collect in the outside curve of rivers. The water itself is not a concern. If you are near the source of contamination, a water filter will remove any contamination, but the filter itself becomes concentrated with any radioactive particles that it has filtered from the water. Treat the filter with extreme caution and keep it away from living tissue. Damn, at this rate we are all going to need portable geiger counters or TLD's with readers.