I'm not sure it's actually 'lying', Chris - the nuke industry is behind the 8-ball. Radiaion and contamination are technical issues - most folk live in a talking-point based world, and "don't have time" for the details.
Doing a quick internet search -
The radioactive decay product of tritium is a low energy beta that cannot penetrate the outer dead layer of human skin. Therefore, the main hazard associated with tritium is internal exposure.
Strontium-90, a radioactive isotope of strontium, is a common product of nuclear explosions. It has a half-life of about 28.8 years and decays into yttrium-90 through beta decay. Strontium-90 is especially deadly since it has a relatively long half-life, is strongly radioactive and is absorbed by the body, where it accumulates in the skeletal system. The radiation affects the production of new blood cells, which eventually leads to death.
Notice that strontium is also a beta emitter, which cannot penetrate dead skin - it's the internal threat that counts here.
bottom line - So type of radiation doesn't penetrate clothing or dead skin, so swimming (or showers) in water with detectible quantities are not considered health risks. Apparently, only those who drink a couple of hundred gallons Hudson river water from the Indian Point area, in a short period of time, may have a possibility of health problems in the future . . ..(I hope that sounds as stupid when it's read, as it did when I wrote it!)