I suspect perhaps that metal plate is precisely what is connecting the ground connections to each other electrically--that, in addition to whatever other functions it may serve, it's a jumper connection. It does look like a rather questionable design given its proximity to the terminal connections; you're right that you don't want the (non-ground) wires shorting out to it.
Does the cover you removed have a plastic tongue that comes between the terminals and this plate? If not, putting in some sort of insulator would be a good idea, as likewise would being precise with how long of a stripped section you make on the wires.