I found a workaround for this.
Firstly: It seems there must exist a metadata file for the item you're trying to import metadata to. For instance, for an MXD there should be a similarily named XML-file (look at the directory in Windows explorer, not ArcCatalog, as that hides the XML-files).
Secondly: In the Import metadata-dialogue: make sure Target Metadata is an XML-file. I tried to import metadata straight to the MXD, but that didn't work. I cannot see the XML files when I browse from the Import Metadata-dialogue, so I just wrote ".xml" after the MXD's path.
Turid