edit-too-late-to-edit: I remembered something that makes me think it's actually more complicated.

If I write 0 and 1 on two different pieces of paper, then flip a coin to decide which paper to give you, we have "entangled" unknowns. When I reveal my paper, we instantly know what's on yours. The joint distribution can't be described per-particle, but we don't consider it spooky. So I think there's something more to it.