In essence the teacher did go to the parents first. That is what the "permission" slip is. I think a missing piece here is how the teacher got to this point in the first place, ie she realized from conversations (this is all hypothetical) that 1) many of the kids at school are going target shooting with their parents (hopefully) 2) that one boy wasn't getting this opportunity but seemed interested in doing so 3) with an opportunity to support the development of the young man offered to the parents in the permission slip. The parents at that point could decline, end of story. They could also express that this isn't the kind of reward but really I see here parents that either didn't know their son was interested in this activity or knew and don't approve. My only issue is that is an expensive gift between a teacher and a student and in today's times is that appropriate.
Now, if this was back 40+ years ago, the school would start an after school target shooting club (with .22 rifles)