If the seed is the same, but the procedural elements are generated on the fly on your hard drive then how would they meet up? Would that not cause synchronization issues? For instance it is possible that there's a storm on one players computer and clear weather on another? If the former player let his life support run out and he died would the other character just fall over dead (or turn into a gravestone) on the latter's screen?
If HG has said it's not instanced then I stand corrected.
The procedural elements are what use the seed and they are the things that will be the same for everyone. Storms are probably random, not procedural, but they wouldn't really cause any issues. What do I care if another player is seeing grass whip around and I'm not?
I would expect the MP, if it exists, to be pretty simple. At the most basic level it just needs to show the position and orientation of the other player. If the other person died they probably would just disappear. How that situation is handled has nothing to do with whether the game is instanced or not though.
What would be weird is if you blew a big hole in the ground, and since that is not synced, the other player would see you falling into solid earth as you jumped into it.