Oh, now I understand, the release that you're trying to change isn't in the MusicBrainz database. I thought it was just missing the cover image.
To be honest, Picard is not the ideal tagger for a job like this. I would use your musicplayer (that probably has this functionality built in) or something like mp3tag. The main use of Picard is that it syncs with the MusicBrainz database.
I tested it out, and you do get the same issue if you're matching a track to MB, and trying to replace MBs cover art.
In that case, if you go to Options > Cover Art, and then untick all the 'cover art providers' except for 'local files', it will only embed the image/s you've dragged in. But I don't think that will solve your problem (trying to overwrite local files).