I'm not sure this is quite true.

Both in hot shutdown and in cold shutdown the reactor is subcritical. The heat comes from the alpha and beta decay of the fission products, but also from the spontaneous fission events of some isotopes (like Pu-240). A fresh reactor core has neither fission products nor Pu-240. But a core that has run for some time has both, although significantly more fission products than Pu-240. Alpha and beta decay events will be more numerous, but less energetic (about 1 MeV). Spontaneous fission events will be less numerous but more energetic (about 200 MeV). Still, by themselves they would generate much less energy than the alpha and beta decay.

But where the story changes is that the spontaneous fission events do generate chain reactions. In a subcritical reactor the k constant (how many more fission events are in each generation) is less than 1. But it makes a huge difference if k = 0 or k = 0.99. If k=0 each spontaneous fission event triggers no other fission event. But if k=0.99, each spontaneous fission even triggers 0.99 subsequent fissions, which trigger about 0.98 new fission, etc. The sum of the geometric series is 100. So overall one spontaneous fission event triggers 100 fission events over a long enough time span.

You control the temperature of the core during a shutdown not by how much heat you remove, but by how low the reactivity k you set. You set the reactivity to a certain level by adding more neutron absorbers, which you do via cadmium control rods or boron injected in the water moderator. If you lower all the control rods and you inject a lot of boron, you get a k of zero. The thermal power produced by the core will get to about 10% of the full thermal power produced during normal reactor operation, so you need to continue to cool the core vigorously, otherwise you get a meltdown. But this power is reduced to much lower levels in a matter of hours. After that, you still need to cool the reactor, but you can use water at normal pressure levels (1atm) rather than pressurized water, and the cooling water would not be boiling.

In a hot shutdown situation you have a non-zero k, which makes the spontaneous fission events trigger sufficient subsequent events that the reactor continues to generate power for a very long time (basically indefinitely). Except that the level of power is much lower than during normal operations, maybe about 10%. This requires active cooling with pressurized water. A sudden loss of power can result in a core meltdown.

That's the problem at Zaporizhzhia: one reactor is kept in hot shutdown, and you have a problem with the cooling because soldiers shoot at each other, then a core meltdown is possible. The Russians prefer a hot shutdown because that reactor allows them to run the systems at the other reactors (under cold shutdown) without needing to invest money to do anything new. The IAEA is telling them: why don't you bring in a new Diesel generator and put this reactor in cold shutdown. To which the Russians are basically answering "Do you mean we need to pay money for both a generator and the Diesel fuel for that generator for as long as this war keeps going? That's a lot of money, money that we could save by keeping this little reactor in hot shutdown. And if the Ukrainians are attacking, it's their fault anyway if anything goes sideways, right?".