No they are technically correct. In the reactor world "shut down" explicitly and specifically refers to chain-reaction-running mode. The reactors do still require active cooling for several days+ to avoid plant damage scenarios. Several comments on this page seem to not have a clear understanding of this difference.
Once the chain reaction is shut down - there is basically no way for the reactor to come alive (chain-reaction-wise) again on its own - not even if it's being bombed, shelled, etc. And run-away super(prompt)critical reactions are not even possible with this reactor design. These reactors are water-moderated - which means that water is used to slow down neutrons to increase their reaction probability. As the reactor heats up, the water gets less dense (even if it is still a liquid) making it a less effective moderator - this density decrease is enough to passively/automatically keep the reactor in a shut-down state. Residual decay heat from radioactivity of the fission byproducts post-shutdown is enough to damage the reactor internals for several days - hence the need for active cooling post-shutdown.
I've seen lots of crazy-exaggerated news reporting on how "bad" or "dangerous" this entire situation could be. It's not good, but neither is the war in Ukraine. It's not even remotely possible for this to be anything like Chernobyl, and I think unlikely to be nearly as bad as Fukushima (which in the grand scheme of the Tsunami - wasn't really that bad). In the war context, I don't think this nuclear plant situation is particularly notable beyond it providing a large fraction of Ukraine's power.
Once the chain reaction is shut down - there is basically no way for the reactor to come alive (chain-reaction-wise) again on its own - not even if it's being bombed, shelled, etc. And run-away super(prompt)critical reactions are not even possible with this reactor design. These reactors are water-moderated - which means that water is used to slow down neutrons to increase their reaction probability. As the reactor heats up, the water gets less dense (even if it is still a liquid) making it a less effective moderator - this density decrease is enough to passively/automatically keep the reactor in a shut-down state. Residual decay heat from radioactivity of the fission byproducts post-shutdown is enough to damage the reactor internals for several days - hence the need for active cooling post-shutdown.
I've seen lots of crazy-exaggerated news reporting on how "bad" or "dangerous" this entire situation could be. It's not good, but neither is the war in Ukraine. It's not even remotely possible for this to be anything like Chernobyl, and I think unlikely to be nearly as bad as Fukushima (which in the grand scheme of the Tsunami - wasn't really that bad). In the war context, I don't think this nuclear plant situation is particularly notable beyond it providing a large fraction of Ukraine's power.
I am a nuclear engineer FWIW.