Exporting related contact's information on a contact that is a subtype

As noted on StackExchange:
We have a relationship type that is designated between a "Student" subtype of Individual and a "School" subtype of Organization ("Student of/Student is"). When we do a search for Students and try to export the School name via the relationship, we find that the "Student of" relationship does not show up in the fields available for export so we cannot select "Student of > Organization Name" as an export field.

However, if we modify the relationship so that it is for all Individuals rather than just for Students, it shows up.