I have a user brftv on my linux system and I have www-data that runs the nginx.
from the terminal I can let my brftv user run
sudo /sbin/reboot
The only way I got this to work on my system was to "hack" it by changing chmod on /sbin/reboot like this guy did
http://linux.byexamples.com/archives/315/how-to-shutdown-and-reboot-without-sudo-password/
sudo chmod u+s /sbin/reboot
I realize this might not be optimal in many cases, but this mediaPlayer is very much locked down so there is no accessing a terminal for anyone else anyways.