IT kind of is true. Sure the death count directly attributable to nuclear reactors is low. But Fukushima caused the entire countries fleet to shut down - to the present day. Safety isn't about lives lost or health, it's about financial repurcussions of the accidents - both directly at the site (take a look at Fukushima today) and the effects on the wider industry, shutting down all the surrounding power plants, and forcing Japan to import fossils to compensate.
And in the 60s the nuclear industry was just as confident of its own safety as it is today.
The only measure of nuclear safety I trust is the liability cap. Currently in America it stands at 0.04% ($300 million) the cost of 1 Fukushima ($800 billion).
But they didn’t. Because it cost money. Because the cost of building a new reactor was so large that they decided to take risks and run the old one past it’s lifetime.
Fast forward to today, where governments are now facing pressure to extend the life of old existing nuclear plants past their shutdown date to reduce dependence on gas.
I don't think it's wrong to call them safer. The point is that the older designs were more than safe enough to keep risks considerably lower than hydroelectricity and fossil fuels.
It's like saying new t-shirts are more wearable.