The specific radioactive pollutant I'm speaking of is tritium which has been found in discharge water from 45 of 65 tested US nuclear sites.[0] Tritum's half-life is more than 12 years, not a few minutes. [ibid]
Several studies have found a connection between ingestion of tritium-contamined water and health effects, including DNA damage that leads to increased infant mortality. [1][2]
Tritium isn't really a "separate chemical" but rather an isotope of hydrogen. Since water molecules are made of hydrogen and oxygen bound together, there is no simple way to remove the radioactive hydrogen by itself. The current best methods, from what I'm seeing online, involve separating the hydrogen and oxygen atoms into gasses and then processing out the tritiated hydrogen molecules. Apparently, it's expensive and only about 85% effective.
Several studies have found a connection between ingestion of tritium-contamined water and health effects, including DNA damage that leads to increased infant mortality. [1][2]
[0] https://en.wikipedia.org/wiki/Tritium
[1] http://www.ccnr.org/tritium_1.html#BEIR
[2] http://www.ccnr.org/tritium_1.html#UN-H