Maybe it's a pet peeve of mine but the onus is not on public health institutions to prove or disprove a negative. Saying "There's not evidence of the virus _not_ spreading in Cohort X" is an almost impossible position. If you have evidence to show it's spreading, then present it, and make public policy decisions based on said evidence. If you don't have evidence, then you should not be making policy.
If you read between the lines the study makes quite a few points consistent with my argument:
> Primary schools may be generally less affected than secondary schools (20, 25–28), perhaps partly because children under the age of 12 are less susceptible to SARS-CoV-2 (29).
The study also goes on to state, in a profound bit of self-awareness:
> Our approach cannot distinguish direct effects on transmission in schools and universities from indirect effects, such as the general population behaving more cautiously after school closures signaled the gravity of the pandemic. Additionally, because school and university closures were implemented on the same day or in close succession in most of the countries we studied, our approach cannot distinguish their individual effects
And:
> (iii) Our results cannot be used without qualification to predict the effect of lifting NPIs. For example, closing schools and universities in conjunction seems to have greatly reduced transmission, but this does not mean that reopening them will necessarily cause infections to soar.
Like stated above, this doesn't prove or disprove a negative. If someone comes out with a direct, causative relationship between re-opening schools and increased infections, and that is reproducible, sure, make policy decisions based on that information. But otherwise, if we are blindly making decisions that can affect the health and development of children, we better have data to back up those decisions.
The clear solution is to test. Look for a suitable district that wants to open up the schools, open them up for a bit and do a rapid lockdown if it instigates an outbreak.
Thats not true when it comes to public health, often it is better policy to act as though the worst case scenario is true, because the consequences of overreacting are far less bad than the consequences of underreacting
