Well and as anything radiation it is always a question of how you come into touch with it.

E.g. getting hit by radiation briefly from the outside is different than having a radiation source inside your body for potentially ever (heavy metals are known to do this).

I am not sure how it is with mushrooms, but as someone who grew up in the Austrian South with similar laws regulating mushrooms I think this was the reasoning. So not that the radiation dose of one of those mushrooms would be problematic, but that it contains radiating particles that happily enter, but not so happily exit your body.

And what is the alternative explanation for the higher risk?