Also, the exposition suggests that this is somehow particularly necessary for visual information because we can't see while sleeping. They originally suggest that this is because it's dark at night, but later modify it to be because one's eyes are closed while sleeping. However, to my knowledge, very little hearing is done while one is sleeping, certainly not enough to protect the auditory portions of the brain from being taken over. Furthermore, if other senses like hearing or smelling are in fact unused while sleeping, it seems like there wouldn't be much need to protect certain regions of the brain from takeover, since there would be no other sense to take them over. Finally, it seems like there are multiple situations where senses are required in a periodic way, such as an animal active during dusk, where its senses transition from being more to less sight focused. Being able to cycle the role of brain regions in response to these changes would be widely beneficial, and we would expect the capacity for this to be deeply ingrained. Insofar as we need non-sight senses while we are sleeping, it seems like the circuitry to deal with cyclic use of senses would be able to protect the visual cortex from total reuse.
Stronger than all this, it seems like REM is fairly fundamental to sleep, in that understanding it ought to offer deep insight into why we sleep in the first place. The proposed explanation offers no such insight, and generally answers no other questions besides the one regarding dreams. It seems like answers to deep questions usually provide insight into questions we didn't even know we had, whereas this answer provides no such insight.
I saw an answer to the dreams question to the effect that the brain cools down while we are sleeping, and REM sleep heats up the brain to prevent it from becoming too cold. This answer potentially provides insight into why we sleep, in that it proposes the cooling of the brain to be important to sleep, rather than incidental. It also explains why interrupting REM would kill a person. It doesn't obviously preference visual portions of the brain, suggesting that visual information is the focus of the brain simply because it is what the brain focuses on while awake. It potentially explains the data of these researchers, if the brain cools down more during sleep whenever the brain is more flexible.
I am not suggesting that I think this answer is definitely true, but merely trying to demonstrate that the standard I am measuring this new theory against is not impossible to reach. I think the explanation of why we dream will look more like the brain cooling answer, rather than the brain reuse answer.