"administer files" allows to delete any file from the "Delete selected file" operation on admin/content/file, even if there is no permission delete specific files, and call to file/%file/delete gives "Access denied" page.
According to https://drupal.org/node/1958950, "administer files" is not a permission that will grant unrestricted access to all files, and instead, it gives access to alter anything on the files that you have access to.

https://drupal.org/files/issues/Screenshot%20from%202014-05-13%2018%3A59...
https://drupal.org/files/issues/Screenshot%20from%202014-05-13%2018%3A59...
https://drupal.org/files/issues/Screenshot%20from%202014-05-13%2019%3A09...

CommentFileSizeAuthor
Screenshot from 2014-05-13 19:09:03.png6.37 KBMiroslavBanov
Screenshot from 2014-05-13 18:59:08.png16.26 KBMiroslavBanov
Screenshot from 2014-05-13 18:59:02.png17.15 KBMiroslavBanov
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Comments

MiroslavBanov’s picture

MiroslavBanov CreditAttribution: MiroslavBanov commented
Issue summary: View changes
Devin Carlson’s picture

Devin Carlson CreditAttribution: Devin Carlson commented
Status: Active » Closed (works as designed)

This works as designed. Unfortunately, as with the content overview page, comment overview page and user overview page, there is no access API for "Update Options". Users only need the administer nodes/users/comments/files permission to be able to use any of the update options.

I'd suggest implementing hook_form_alter() to tailor the options based on your requirements.