The thing linked to doesn't show it not to be true. It gives point estimates of 0.03 deaths per TWh for nuclear and 0.02 deaths per TWh for solar (and higher figures for everything else) and says "the uncertainties around these values mean they are likely to overlap".

So it indeed doesn't show that "nuclear is the safest" is true, and if forced to guess on the basis of the numbers there you'd do best to guess that actually it's second-safest after solar, but it also doesn't show that "nuclear is the safest" is false" and a more accurate description would be "wind, nuclear and solar are all comparable to one another, and all much much much safer than any fossil fuels, there probably isn't that much difference between them, and we don't really have the data to tell what order they should go in".

(Some slightly more concrete numbers: total electricity generation of the US is about 4000 TWh, so those figures suggest an average of about 120 deaths per year if that were all nuclear and about 90 deaths per year if it were all solar. For comparison, according to https://www.statista.com/chart/6024/causes-of-death-in-the-u... these are on the same order of magnitude as "deaths by lawnmower" and "deaths by autoerotic asphyxiation".)

It would probably have been better to say something like "the safest, along with solar and wind power". But everything we know is perfectly compatible with nuclear in fact being the safest, or the second safest, or the third safest.