The most likely cause of this is that Word is NOT running as the user you think it is.
This can often happen if your running Word (and other apps) from a dedicated application server, which may be being accessed with a differently impersonated set of credentials than the credentials that your user is logged in with.
A quick and reasonably foolproof way to check this, is to set up a linux samba server and attach it to the same AD, save a file from word into a share on that samba server, then log into the Linux command line, list the files and see exactly what user it believes the file was saved as.
This works better than saving it on a windows machine, because in the windows environment impersonation gets in the way and can often label a file with the intended user, but impersonate with a different security SID.
Things to look at:
Check the user that word is running as
Compare the user that word files are saved as, with files that are saved from desktop
Temporarily set user permissions on a user share to "Everyone, Full control" then re-test a save in word does it work? (If it does then it's screaming out that it's a user impersonation problem)