Hi,
Should an account configured with the standard "user" role have the ability to set permissions on their own field extractions? I have a customer who created some field extractions, but made them private, and isn't allowed to change the permissions on those extractions.
No. Users are not allowed to change permissions. So far as I can tell, the admin_all_objects capability needs to be added to the User Role for users to be able to change permissions on searches they create.