I have permission - Import media files from the local filesystem
Simple file importer - set for admin only but an authenticated user can, while editing/changing/uploading a media field, browse through the entire site's library of uploaded images, vids, etc. rather than just their own media files.

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Devin Carlson’s picture

Devin Carlson CreditAttribution: Devin Carlson commented
Title: Authenticated role able to see all media files » Authenticated role able to see all files
Project: D7 Media » File Entity (fieldable files)
Version: 7.x-2.0-unstable5 » 7.x-2.0-unstable6
Component: Media Browser » Code
Category: bug » feature
Status: Active » Closed (duplicate)

This is a File Entity feature request.

There is currently no way to restrict users to their own files. I believe #1227706: Add a file entity access API is what you're looking for.