The doctor who ran the study said this:
I would put a little asterisk by that and say that yes, there is a possibility that there’s an asymptomatic student who has given it to a teacher and we don’t really know, because I don’t know the source of infection in every case. But there’s no evidence of that. In most cases, the infection could be traced to a family member or a friend where they had spent time together outside of school. In some cases, sports activities, carpooling, and social gatherings were identified as the sources of infection.
Given that for known infections, they were acquired outside of school at a much higher clip than within school, why would it be any different for undetected infections? Presumably contact tracing involved testing kids who were in class with infected people (the article mentions setting up in-school saliva testing) whereas kids who have contact with infected people outside school aren’t always informed or tested. So if anything, we’d expect infections acquired at school to be detected more frequently, in percentage terms, than those acquired outside.