Clients always receive updates about other clients after the Server has told them about it, but then so does character movement (non-physics) and there’s nothing you can do about that. The Server is also behind too.
The client-authoritative solution applies to the local client only, and it solves the problem of constant rubber-banding (being snapped back to a previous location each time you get a server update). All it means is that the client who posesses a pawn is in charge of where that pawn is, not the Server.
The problem with that of course, is that cheating is incredibly easy.