If business software practices is not enough of a proof, look at any massive online games. They all use one central server as a source of truth about the game world, and broadcast that state to the clients. Anything a client reports that diverges from the central server view is either corrected, rejected, or becomes a reason to disconnect the client for cheating attempts.

If you need strict order, that order should happen in strictly one place. (The universe itself does not support strict order at a distance, as Special Relativity shows.)