Do you know for sure that the check they intend to do is all-encompassing?
It seems odd that they'd need to know much other than your criminal background, particularly if you are a volunteer.
If they are working at the school, they've had the same or harsher background check done on them. That doesn't mean that you are priviledged to the details of that information - only to know that they passed which is evidenced by them working there (I would hope!). And I am sure that these don't get passed around. It's probable that the only person who would see the details would be the principal and maybe his/her secretary (I don't think schools have dedicated HR people, but I don't know for sure).
I guess I'm wondering why it would be a big deal? Other than asking them how they maintain your privacy (who will see it and how will it be safeguarded after the fact) I don't see any issue.
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