We must be watching different movies, because the intro with Hiroki as an adult and at the abandoned station, he doesn't talk about her at all. All he says it, "On that day long ago, beyond those clouds, lies the place of our promise." If you were talking about when he actually narrates when the actual beginning of the story starts, that is another story. He does refer to her directly, and he refers to her like she's alive, because in the beginning of the story she is alive. It'd be silly if he were to introduce her character, and say that she had died or something from the get go.

You can assert your ending that way. This is an open ending, you do not see them grow old together, or get married or have kids. You just see Sayuri crying on the plane, and it cuts out. By waking Sayuri from the dream, by bringing her to the tower they lost their promised place, being the tower. The tower held all their dream, aspirations, and it was just a sign of something that was theirs, and theirs alone even if in their own world. We don't see her die at the ending, but Hiroki just says "we may have lost our promised place, but our lives begin now.", leaving the ending a pretty wide open ending.