How to : grant access to a private file for certain roles when serving of private files is disabled ?

Hi,

I have a role Member.
On a page that only members can view, I have added a link to a PDF file inside the body field.
I don't want anonymous users to be able to access the PDF if they know its URL so I put the PDF in my private file system directory so the href is /system/files/myfile.pdf
Because I don't want my Backup & Migrate backups to be accessible by anonymous users I checked the "Disable serving of private files" checkbox.
But now nobody even user 1 can access /system/files/myfile.pdf
How can I tell Drupal that users with certain roles can actually access this PDF ?

Thank you !