Naturally I don't know which particular study the author meant, and a large number examines the relationship between being distracted and boredom (a single search revealed hundreds), but this one particularly came to mind (The experience of boredom: The role of the self-perception of attention. Damrad-Frye, Robin; Laird, James D.
Journal of Personality and Social Psychology, Vol 57(2), Aug 1989, 315-320.):
Ss in a listening situation were simultaneously distracted (a) not at all, (b) moderately, or (c) loudly. As hypothesized, Ss who were distracted by extraneous noise at levels too low to be recognized as a distraction reported that they felt more bored and that the task was less pleasant. That is, they attributed their inattention to the material as opposed to the distraction. Extraverts required louder distractions than introverts to produce boredom.
More on boredom and attention in LePera's Relationships between boredom proneness, mindfulness, anxiety, depression, and substance use (1):
According to the attentional theory of boredom proneness,
boredom results from a deficit in attention (Harris, 2000). The current study investigated the relationship between mindfulness (the ability to attend to the immediate environment) and boredom proneness [...]
It also seems people judge the attractiveness of a task based on the particular distractions they've experienced (2):
Four studies tested whether people also rely on unobservable “behavior,” their mindwandering, when making such inferences. It is proposed here that people rely on the content of their mindwandering to decide whether it reflects boredom with an ongoing task or a reverie’s irresistible pull. Having the mind wander to positive events, to concurrent as opposed to past activities, and to many events rather than just one tends to be attributed to boredom and therefore leads to perceived dissatisfaction with an ongoing task