@ntozier is correct, you need to use
setup/scripts/rcron.php for remote cron calls. If you want to use the actual
api/cron.php file you must use Cron or Crontab. An example Crontab entry for this would be like:
*/1 * * * * root /usr/bin/php /path/to/osTicket/api/cron.php
The documentation is outdated for this particular case and we will update this to reflect what @ntozier and I said here.