Of course it matters.
The question is obviously referring to a serious infraction as described by their examples: “. . . probation, suspension, removal, dismissal, or expulsion . . .” The incident described by this student doesn’t come remotely close to any of these. If, furthermore, the school doesn’t even note it on the permanent record, they clearly consider it to be a minor matter not worth mentioning. So, I don’t see that it needs to be mentioned in that case.
No one here knows the full circumstances of what happened. Nobody here knows the full extent to which instructions for the “open note” exam were explained to the students. For all we know, the fault lay with the teacher and that teacher is in trouble with his/her supervisor, and the school went ahead with a perfunctory action just to get the point across to the students. The point is that no one here knows what went on behind closed doors at the school.
IMO, we have no business advising this student on her question because we don’t have sufficient information. I think the best advice was @Bruno99’s suggestion that she ask her school counselor.