So make the owners of renewables liable too? From what I know ONLY nuclear has that stipulation.

Are they not? Coal has certainly been exempt in most places.

A solar plant is certainly liable if accidents happen on its grounds. They don't need insurance against a major disaster like a meltdown because it can't happen.

Nuclear is NOT liable for a major nuclear disaster. No insurance would cover it. So I don't know where you got your knowledge from but it is not based on fact.

Edit: OK I should have been clearer. They are liable like everyone else. They have (unlike solar installations I suspect) strict liability which means the damaged person does not have to prove fault. However, the amount of liability is limited (in time and amount) and the state takes over. This is what I was referring to with they don't have liability (admittedly incorrect the way I wrote it).

Source:https://world-nuclear.org/information-library/safety-and-sec...

The problem with nuclear liability is that there are potential accidents that are both extremely rare and extremely expensive. Such accidents have only happened twice. This creates some difficulty for calculating insurance premiums.

The article you linked says that TEPCO paid out USD ~65 billion after Fukushima, but it was insured only for USD ~804 million.

Naturally what happened is that the government didn't want to be without electricity, so to prevent bankruptcy TEPCO was nationalized. This is the typical scenario for nuclear power: profits are privatized while losses are socialized.