If you don't have access to the file system on the server for a Drupal site, when a security issue like Drupalgeddon2 comes along, you are entitled to panic! Many sites are run by a combination of teams, so sometimes you really don't have control over the server... but that might even mean there is another way to apply fixes. If you've been tasked with updating such a site (I was!), it's worth checking if the server has been misconfigured in such a way to actually allow you to patch Drupal, via Drupal!
A heavy caveat first: we would never...