The author says the waste isn't liquid, but also says that spent fuel rods are cooled in pools for several years. Does the water not become irradiated in that time?
Here's a paper on how water gets activated when it cools a nuclear core (which does have massive numbers of neutrons zipping around): https://doi.org/10.1016/j.pnucene.2019.103042
Assuming the fuel rods have intact cladding, then the first shouldn't be happening in a cooling pond. However the fuel rods do give off neutron radiation, and a small amount of the hydrogen in the water is turned into tritium by that neutron radiation. Tritium is a weak beta emitter, it could harm you if you drank a lot of it. But it's not a long-term problem because it has a half life of 12 years.
I think the water is mostly safe. At worst the water will have little slivers of radioactive material floating in it but that’s only if something already went wrong, so I imagine it’s cleaned before being discharged.
Ultimately you can also cool it down and reuse it, so you might not need all that much water relatively speaking.
But that wasn't the point being made here. The point being made with the hot spoon example is that EM radiation doesn't make other things radioactive (except insofar as it heats things up). This is equally true of gamma radiation as thermal radiation. Thermal radiation and gamma radiation can both cause harm directly, but neither will make other things radioactive.
That's why it's completely safe to eat food that was sterilized with gamma radiation intense enough to kill you outright.
Here's an example:
"Photonuclear production of medical isotopes 62,64Cu using intense laser-plasma electron source"
There's plutonium dust in the silt under the Irish Sea, off the coast from Sellafield. Inhaling a single particle of plutonium dust (much smaller than a 'sliver') can kill you. I think your imagination has misled you.