Change WordPress user roles and capabilities › Forums › Bug Reports › Delete upload files permission › Reply To: Delete upload files permission
In general, user should be capable to edit post to which media file is attached. It it’s true, user can edit this media file (attachment) property and delete it. ‘upload_files’ allows just to add new item to the media library.
If you turn ON the “Force custom post types to use their own capabilities” checkbox at the “Settings->User Role Editor->Additional Modules” tab, then WordPress will check ‘delete_attachments” capability instead of ‘delete_posts’. So you have to look if required capabilities from the “Attachments” group were granted to a role or user.
Some plugin can introduce a problem also. So all plugin temporal deactivation may help to isolate a reason.