OK - talked to the School superintendent today, so I have more information.
He said they have determined that there have been a few cases of in-school transmission, because contact tracing could not detect any other possible source.
Also, from what he said, if a student tests positive, and that student was in the same classroom all day, everyone in that classroom has to quarantine. I do not know if that policy is unique to this school or if it is recommended by the State Dept of Ed or State Dept of health.
I specifically asked him if this was a "conservative" or "cautious" policy, and he agreed that it was. (and yes, I was thinking of you when I asked that question!)
But he also said that he is responsible for other people's children, and he has to be cautious about anything pertaining to their health and safety.