Spooky action at a distance in general probabilistic theories

We call a probabilistic theory complete if it cannot be further refined by no-signaling hidden-variable models, and name a theory spooky if every equivalent hidden-variable model violates Shimonys Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schrodinger. Finally we show that steering of complementary states leads to a Schrodingers cat-like paradox.