Almost all computers are insecure, not just the systems in nuclear stations.

Most operating systems are based on ambient authority, which is just a disaster waiting to happen.

What's the alternative?

I built control computers for nuclear reactors. Those machines are not connected to a network and are guarded by multiple stages of men with automatic machine guns. It was designed to flawlessly run 3x boards each with triple-modular-redundant processors in FPGA fabric all nine processors instruction-synced with ECC down to the Registers (including cycling the three areas of programmable fabric on the FPGAs). They cycle and test each board every month.

What’s your source?

Well, the news says that doge randos are potentially exfiltrating the details of systems like that as well as financial details of many Americans, including those who hold machine guns and probably suffer from substandard pay and bad economic prospects/job security as much as anyone else does.

Perhaps the safest assumption is that system reliability ultimately depends on quite a lot of factors that are not purely about careful engineering.

Nothing like a special commando of people doing your more malicious biddings while also being expendable

A bit off topic, but my uncle used to be security at a nuclear plant. Each year the Delta Force (his words) would conduct a surprise pentest. He said that although they were always tipped off, they never stopped them.

How is the software inspected and tested for defects, malicious or accidental? I'm just very curious about how this is done.

I guess the biggest security advantage of any of these old critical systems is fact that they are not connected to the internet. At least I hope they are not.