Edit own files permission not giving 'Edit media' link for media fields in node edit form

We are seeing the new file_entity_access working only partially on media fields.

We have permissions set up under the new file_entity permissions system so that admins on our system can edit and delete all files, but student users can only edit and delete their own. The permissions are working properly on file entities but we are only seeing partial integration into media fields.

User 1 is seeing 'Edit media' links in media fields in node edit forms with media, but students are not seeing 'Edit media' links when they own files.

Admins are also not seeing 'Edit media' links.

Students have the new permission 'Edit own files' and admins have 'Administer files'