The study participants were split into two groups. One group solved the problem alone, in silence. The other group was instructed to narrate their thought process out loud to an interviewer who stood over their shoulder (literally, see the photo on page 3) while they solved it.
The flaw in this study is that the two groups weren't really assigned the same task. Solving a problem isn't the same as verbally narrating your solution to a problem. The authors attributed the differences not to the extra work narration work assigned to the second group, but to anxiety levels.
The participants even explained that their difficulty came from having to talk while solving:
> Participants also had difficulty with performing tasks that involved multiple simultaneous actions. Participants felt stressed by having to “talk while trying to write” (P44), “talking while writing” (P25), and “think and talk and do code at the same time” (P39). P41 found it difficult to “constantly speak during solving” and “lost breath at a few places during the task”.
There are other concerns with the study format such as many of a significant number of participants simply giving up well before the clock ran out, in both the private and public interview groups. They were given 30 minutes to solve 3 problems, but some of the participants (including in the private group) were giving up around the 10 minute mark without solving anything at all. This suggests a very high variance of the underlying abilities of their candidates, which necessitates a much larger sample size to draw conclusions.