I've tested some more,
If you in Company Home for test purposes create a space, lets call it Test. Give the user you are accessing that folder via CIFS Collaborator rights on the Space. You can do that using Alfresco Explorer or Share Repository.
Now if you create and edit documents, it works.
If you only assign Collaborator on a specific document, it fails with access denied. Collaborator needs to be set on the space, so that temporary files that are created get Collaborator as well.
Also tested to set only Consumer rights on the Space, and Collaborator on a specific document. In that case you can open the document without error, but you cannot actually save the document. I guess that is hard to workaround, since word wants to write temp files, and you do not have those rights.