In what cases might a volunteer be required to have a background check?

Policy language is intended to be broad and invoke the very thought process you went through. "How might that apply in my circumstances?"
For example, in a case where the Federation might have a volunteer who is assigned to drive a busload of youth somewhere or to supervise a group of youth for an extended time, etc., then the Federation might require a background check beforehand.
At the school level if a school owner has a volunteer helping them that stays overnight with students at the school for a parent's night out or chaperones youth on a camping trip or to the Nationals for a weekend, etc., then the school owner might require a background check beforehand.
There may be some state laws that are even more specific, but this is the Federation's call to awareness for all.