Other than they didn't.

The exact wording was "because Jun doesn't die, so we don't know what happens to him after this." Heavily implying to me that he, well, doesn't die. They could have been referring to the game as much as they could have been referring to post-game. But seeing as all we knew was that A) Bungie said he survives, and B) Halsey is obviously alive, then we could only assume he was alive until proven otherwise. Maybe he could have died in another battle later in the war, but that would have been entirely an assumption, where at least thinking he was alive had some factual backing to it. What mattered is that we knew he survived Reach, which would categorize him as alive until proven dead.