That's not an accurate summary; that should be "having one more doctor tell someone to wear a mask does not have a large enough effect size on their likelihood of getting COVID-19 for this study to detect." They had 1.8% infected in the extra-recommendation group and 2.1% in the control group.
> Based on the lowest adherence reported in the mask group during follow-up, 46% of participants wore the mask as recommended, 47% predominantly as recommended, and 7% not as recommended."
Personally, I find it easy to believe that people were in fact wearing their masks. To be in the study you it looks like you had to joined voluntarily on your own accord, indicating a participant group with an interest in it:
> Recruitment involved media advertisements and contacting private companies and public organizations
If anything, I find it easy to believe that adherence would be less in the general population than in this study. Particularly stuff like wearing masks incorrectly, eg not covering the nose, leaving gaps, etc.
Edit: it actually looks like the study doesn't include that statistic at all, which is appallingly poor design.
Why do you think that? The study says "A total of 3030 participants were randomly assigned to the recommendation to wear face masks, and 2994 were assigned not to wear face masks".
At the time the study was performed (April and May 2020), it was not common to wear masks in Denmark outside of hospitals. In fact the authorities recommended against wearing masks because there was a shortage and the available masks should be reserved for high risk groups.
There is lots of evidence that wearing mask protects others, that's why surgeons wear surgical masks during surgery.
Surgical masks are not intended to protect the wearer, you need medical respirator for that. The question is how effective they are in doing job they are not designed to do. It seems to be limited, maybe around 30-50% depending on the study.
There is a lack of evidence for the effectiveness of masks during surgery, and they aren't always mandatory to wear:
https://www.cochrane.org/CD002929/WOUNDS_disposable-surgical...
https://www.medpagetoday.com/infectiousdisease/infectioncont...
https://ncbi.nlm.nih.gov/pmc/articles/PMC4480558/
There are obvious hygienic benefits - no-one wants to be splashed with bodily fluids - but there is a lack of evidence that they actually protect the patient.
First, it's not testing the efficacy of wearing a mask: it's testing the efficacy of telling someone to wear a mask. This is explicitly stated in the "limitations" section.
Second, getting a decent control group is almost impossible. Essentially no one in modern society is unaware of COVID or the recommendation to wear a mask, and essentially no one had failed to form an opinion on whether or not they will comply with that recommendation. And indeed, "variable adherence" is another factor called out in the limitations.
The summary could be reworded "having one more doctor tell someone to wear a mask does not make them less likely to contract COVID-19."
This study is very much not about the efficacy of state- or nation- wide mask mandates.