real-time notification of file system changes
Even rsync is technically a pull operation, needing to compare each file in both trees to find changes that have happened to them, rather than just knowing such changes in advance.
An approach to knowing such changes in advance is to use version control. Another is to use file system notification like inotify.
Even changes to files on websites (uploaded by ftp for instance, or by a file-based CMS) could be multicast to backup servers or a mirror network, automatically, or according to whatever logic.