Ah, I'm glad you asked that question ...
Yes, two people can order the same dress. I believe in that article a few seasons ago about Susan Casden, she mentioned that she has (negotiates for, demands, read whatever you want into that ...) a West Coast exclusive on the things she buys, something like that. And she is one of the highest-profile HC customers as we all know ...
It's true that you can have the piece customized, but I'm sure some customers feel that what they've seen on the runway is just about perfect in some cases. Other pieces, no one orders.
My guess is that being an established couture buyer in general and at a house in particular helps you get a better exclusive. I don't really see someone coming in to buy their first piece also getting a world-wide exclusive ... perhaps it happens for some customers, but when you think about what the shows cost, and that many houses are not able to recoup those costs, you're asking for quite a lot for one of 45 or so pieces to be made for you only