Drupal - How can I create a download link to a private file?

When I add the field 'File: Download link' to the view it works fine.

The views field handler for the 'File: Download link' has this snippet to check access:

if (!file_entity_access('download', $file)) {
   return;
}

and this snippet to construct the uri for the download link:

$uri = file_entity_download_uri($file);

The code for file_entity_download_uri():

function file_entity_download_uri($file) {
  $uri = array(
    'path' => "file/{$file->fid}/download",
    'options' => array(),
  );
  if (!variable_get('file_entity_allow_insecure_download', FALSE)) {
    $uri['options']['query']['token'] = file_entity_get_download_token($file);
  }
  return $uri;
}

show the download token being added to the options query key of $uri which is returned.

Adding that to the PHP code field:

<?php
    $fid = $row->fid;
    $file = file_load($fid);
    if (file_entity_access('download', $file)) {
        $uri = file_entity_download_uri($file);
        print l(t('Download'), $uri['path'], array('query' => $uri['options']['query']));
    }
?>

results in a download link to the private file.