It's unlikely that there's a remote 'stop burn' option for a coal-burning power plant, for instance.
Many modern control systems *DO* have a remote access capability. This allows engineers to log in remotely to troubleshoot problems.
Some of these control systems are based on Unix variants such as Solaris. Unfortunately, they are often administered by people that are completely unfamiliar with Unix and network security. At least one vendor that I know of asks that you do NOT change the root password on their system so that their support people can dial in and run system tests occasionally as part of their service contract!