To be fair this article doesn't say nuclear energy is safe - rather that it is the safest relative to other sources.

You mention Chernobyl and Fukushima - but those only stand out because the effects were concentrated in time and space (happened all at once and afflicted specific geographical regions).

The deleterious health effects of coal, oil, and natural gas are more diffuse. They don't make such good news stories and there's really no way to build an interested narrative around them. The effects evolve over time, the geographic impact is not as concentrated, and importantly there is a much stronger probabilistic element - the human brain has a hard time processing this, but it has an easy time processing nuclear dangers.