Some repository types support a return type of FILE_REFERENCE. These work as you ask - when the external file changes, the versions of it within Moodle are all updated to match.
Unfortunately, as it is currently implemented, the webdav repository only supports FILE_INTERNAL (the current version of the file is copied from the webdav repository into Moodle, but does not update) and FILE_EXTERNAL (a link to the file in the webdav repository is inserted, but the file itself stays in the webdav repository - I suspect this means that a user viewing the file inside Moodle will need permission to access that particular webdav location in order to see it).
It may be possible to implement FILE_REFERENCE for webdav repositories; I don't know off the top of my head whether or not there are any technical reasons why this wouldn't work. It may simply be that no one has had time / need to implement this yet (in which case, it might be possible to pay for a Moodle developer to implement it for you).