Could you please report it, as it is obviously a bug? In fact, the behaviour of Moodle's File Picker is not what is shown for example in the video which link can be found in the "Working with files" page of Moodle's documentation.
On a fresh installation of Moodle 2.2.1 (nightly build as of today, PHP 5.4.0, mySQL 5.5.20, Windows 2008R2 SP1), with all roles definitions checked and reset to default, I've added two File System repositories, one Google Repository and checked several cases. Another test was done on a similar configuration but with a database upgraded from Moodle 2.0 with many courses, once again after resetting roles capabilities to default.
- For an ordinary student, only the Google Repository appears in the File picker when trying to add a file to its "My private files", which is ok for me.
- It is the same for a user registered as a teacher in some courses trying to add a file to its private file. To my point of view, as long as this user as the editing teacher role, he or she should be able to access all repositories in this case.
- When the same user edits one of the courses in which he ou she as the editing teacher role, then the Server Files repository and the two named File System repositories appear in the File picker (ok) but any attempt to use them ends up with a "No permission to access this repository" message (not ok).
Of course there is a workaround : adding the capability to all Authenticated users to use these repositories but this is not an option for production systems. We do not want all students to have access to all resources of our Moodle site.
By the way: in this configuration, when a user accesses to a resource uploaded by another teacher and tries to insert it into its private files or in its own course, the name of the creator of the original resource and its license type are not preserved. This is incorrect.