I do not doubt Bungie's ability to create a universe on the size that they are talking about, and possibly bigger than that of Halo.
From the very limited information that we have (I think we will not see any more until the reveal of the next xbox), the game sounds like the story will interact with the player, not the other way round. What I mean is that at the moment we as players interact with the story, even with games that extort that they form to players choices. In the end, these choices are limited in number, resulting in scripted endings, whatever the choices you have made in the game, and can sort of make you feel redundant. You still have to interact with certain scripted moments in order for the story for move forwards, going to a certain place, with a certain item, etc, etc. What Destiny sounds like is that they maybe no main quest, as such Bungie have hinted at, I think, and that it is more of what the player makes of their time within the game that makes a story individual to the player.
Bungie maybe making a foundation for players to build upon themselves, that the experiences we have in the game is the story. The only other videogame that I can think of that does this is Minecraft. We are given some historical background, and a physics engine, and then told to explore. If Bungie does this, and pulls off the game play, it will change fundamentally how we play videogames in the future.
Hope I am clear enough
PS. The stuff that Bungie and Activision are putting up at the moment could just be mediaspeak, and that it could be very much on the lines of go there, shoot said alien, do said thing for the story to continue, but I still think that Destiny will be a good game, viewing Bungie's record since 2001. BUT GOD, if Bungie does make it focus around player exploration of a the environment that they build, it would be fantastic.