Make private pdf files Non-Downloadable via absolute url links
It should be as easy as adding an implementation of hook_file_download() to a custom module:

function MYMODULE_file_download($file) {
  // Add whatever other conditions you need to this, e.g. test the
  // file extension for .pdf
  if (user_is_anonymous()) {
    // Deny
    return -1;
  }

  // Allow
  return file_get_content_headers($file);
}