Well, it does and it doesn't. I get that they're two separate things, but it doesn't make sense that they should be.

In the hypothetical you describe, I would just consider the paper to be out-of-date, and the "truth" to be the updated record with the airline. :-) In that respect, I suppose I'm thinking of them more like paper boarding passes. The concept of a ticket separate from the reservation just doesn't seem like it serves a purpose, other than as an artifact of when tickets actually existed. Even then, my mental model would be more like a receipt -- it's your proof that the record said that at some point, in case there's a question.