Even if all that were to happen in the worst possible case scenario (as has happened at Lake Karachay in Russia where untreated nuclear waste leaked into the groundwater in large volumes), it's still a long shot from being as deadly as the fossil fuels we take as a given today. That sets the upper worst hypothetical imaginary case for vitrified nuclear waste if some super volcano erupts at the storage site and converts it back into a chemically active form.
You can buy kitchen plates and glasses made from uranium glass, and that stuff is relatively a bigger hazard than vitrified nuclear waste. So is the americium in your smoke alarm, so are the various nuclear materials used at your local hospital for radiography and radiology.
To really nail this point home: coal fired power plants release more radioactive waste into the environment that nuclear plants do. The trace uranium found in coal can't be combusted and makes its way out the chimney, and that is more than a nuclear plant releases including disposal [1].
[1] https://www.scientificamerican.com/article/coal-ash-is-more-...
Are the coal-produced concentrations of such waste equal or higher than with the nuclear power waste? Say, if somebody is particularly unlucky and digests that?
How do you know? From what I learned, a big problem with spent fuel is radiotoxicity. How do we know that no amount of weakly radioactive, but pretty toxic because of that material made it to the environment? Are all those storage containers that safe?