GitLab

Previously, only apps were allowed to use this api, however most clients will
be actually written as extensions.

This patch has been once reverted due to a bug. See:
https://codereview.chromium.org/527663002/

TEST=browser_tests: *FileSystemProvider*Extension*
BUG=409487

Review URL: https://codereview.chromium.org/537153003

Cr-Commit-Position: refs/heads/master@{#293285}