The fact that we're talking about multiple people looking at the same chat - the fact that we do conceptualise it as "the same chat" and "the history" - implies that we think of it as a single thing. And I think messenger apps generally nudge us that way - e.g. setting the name of the chat usually sets it for everyone.

> It is the order people (and their records, if they have some) would have had in mind in the old time.

I don't think it is. If I pull my correspondence with person X out of my drawer or file, the only dates I have to order them by are the dates written on the letters - which are the letters they and I (if I keep carbons of the ones I send) wrote them on, not the dates I received them. If they sent me a postcard while on holiday and then a letter after returning that arrived sooner, I'll read them in one order on receipt and in a different order when looking back. Likewise if I have a memo of a phone call with them, that may be from before I received a letter that is nevertheless dated earlier.

If it's a system where the server is merely store-and-forward, where it forgets its knowledge of messages after the recipients have received them, then sure, your stance is reasonable. The client will decide on message ordering; it can either just display in the order received from the server, or use any timestamps stored in the messages to order them (including possibly reordering if messages arrive out of order). The client has no other source of truth it can draw from, and so different clients may order things differently. (Even in this case, though, for many systems like this I would expect the server to timestamp the messages, and for all clients to honor those timestamps, so in practice everyone should see the same ordering.)

But Matrix is not such a system: each homeserver is the system of record for what messages have been received, and what order they go in. In this case, I would expect all users to see the same ordering, assuming all clients are able to query and receive the full history from the server.