This would have been a perfect opportunity to cite the paper about the efficacy of parachutes: https://www.bmj.com/content/363/bmj.k5094
The "Parachutes" paper is demonstrating that parachutes make no difference when used out of a stationary grounded plane.
I think the point is that both papers are demonstrating that the numbers alone don't tell the full story.
When beliefs regarding the effectiveness of an intervention exist in the community, randomized trials might selectively enroll individuals with a lower perceived likelihood of benefit, thus diminishing the applicability of the results to clinical practice.
So... was there some kind of selective enrollment in the teacher study? I don’t think that’s the issue here.
That skews the results of these studies. This is what they try to illustrate with the jumping out of plane study. The result won't be reliable if you don't have a control group that actually might have benefit from the treatment.
Cancer patients (jumpers), will or will not get a new type of chemotherapy (parachute). But since it is known that the sickest (hightest jumping hight) certainly will die without treatment (parachute), they decide to only test the treatment on patients with only early stage and benign cancer (close to the ground).
Both this article and its predecessor were published in the Christmas issue of the BMJ, where funny papers with a semi-serious point (in these cases, the ongoing debates in medicine about the superiority of RCTs over other forms of clinical evidence) are common.
My favourite of this genre is "Does Peppa Pig encourage inappropriate use of primary care resources?" (https://doi.org/10.1136/bmj.j5397) critiquing the clinical practice of Dr Brown Bear, a fictional cartoon GP.