It's a somewhat unusual request.
Going only by what you have said here,
with the missing facts missing, with no specifics or back story, and
with all the ifs, buts, maybes, unlesses, and exceptions not allowed for,
I don't see how they could have an enforceable right to be a member of the group.
That said, why don't you have a look at the group/ page settings...
and see if you can set them on moderated posting?
Why not set the group to private or secret?
What reason have they given for wanting access?
Have they some sort of reason (to help control counterfeiting, for example)
which is better than "Let me in or I'll report you to Facebook" ?