Check that the service Groups for Business is not turned on for the Student OU (in fact, we turn off that service for most everyone, staff included, unless there is a clear reason why they need that access). That service does not affect whether a user can be in a group, it affects if they have access to groups.google.com and can manage a group they are a part of (most people do not need this type of access).
Make sure that you leave this service on for you and your tech group. Then you can go into that service and look for the group that was affected to review the history and settings for it. One option would be to turn on moderation so that someone (the teacher or principal) can moderate which emails get sent through to that group.
Hopefully this helped answer your question!