They never actually measured the amount of work hours being done remotely. They never measured the number of employees working remotely. They just had some guy make up "remote-ability" numbers for each sector and then carefully pretended to be doing science. Meanwhile all these sectors have seen unrelated changes to operating environment that have not been controlled for. It's BS on BS on BS.
Overall I am not even convinced their remote work metric would correlate with hours worked remotely.
Getting access logs for whether people logged in from home or the office is really not a crazy stretch.
Measuring the dependent variable "productivity" is actually much harder since firm-level productivity (aka earnings) has a whole host of other things that impact it besides worker-level productivity and we all know how hard it is to measure developer productivity.
Just as a really obvious example: tech stocks soared due to the pandemic; was this because WFH was good for tech companies, or was this due to other factors (wfh means people need to buy more tech, low interest rates pumped up all stocks, etc)? I obviously have my own opinion here, but this study design is not strong enough to disentangle any of this.
This study really is total garbage in the vein of "well, our data sucks, but we want to say something" and should not be taken seriously by proponents or detractors of WFH.