Sure; the problem starts here:
Message comes in to sales@
@Sales invites support@
[State: not archived for both]
@Support archives
[State: archived for @Support, not archived for @Sales]
@Sales still sees it, but the button says “Move to Inbox” on the post itself; sales has to do Move To Inbox, then Archive again to actually properly archive it.
(the folks in support don’t have access to sales)