How can I really look at OBN at the database level?
For this, consider using transaction SE16 to look at the database table AGR_HIER_BOR. An OBN call is usually in the format object.method and is stored in the database table in the fields LOBJTYPE_NAME (equal to object in this example) and VERB_NAME (equal to method in this example). By defining a specific query, you can see in which roles this specific OBN target is defined.
You can use transaction SU01 to verify whether the user has found the assigned role.
Additionally, with the key fields AGR_NAME and OBJECT_ID, you can look up the associated application in table AGR_HIER.