This article is teaching me that I misunderstood what the default mode network (DMN) is. I was introduced to the term while reading how psychedelics affect the brain. As I understood it, the DMN is a mediator among the many thoughts that normally compete for your brain's attention. By temporarily suppressing the DMN, psychedelics give the weirder thoughts a better chance at center stage. Thus the black dot on the wall looks more like a spider, and a normally tenuous connection between Concept X and Concept Y might lead someone to discover a mechanism for cold fusion while tripping.
This article's explanation, on the other hand, fits the DMN moniker better: it's what your brain does when it isn't doing anything. If psychedelics replace a default value with an uninitialized variable, then the resulting behavior is undefined.
This would explain why so-called "set and setting" are so important while experiencing psychedelics. A preoccupied mind doesn't use the DMN. So it would follow that a preoccupied mind wouldn't benefit as much from a suppressed DMN, because it wouldn't have any reason to try activating it.