[3] The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin".
The Min axiom asserts only that two experimenters separated in a space-like way can make choices of measurements independently of each other.
Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe's past in an ad hoc way.
As stated by Cator and Landsman regarding hidden-variable theories:[4] "There has been a similar tension between the idea that the hidden variables (in the pertinent causal past) should on the one hand include all ontological information relevant to the experiment, but on the other hand should leave the experimenters free to choose any settings they like."
According to Cator and Landsman,[4] Conway and Kochen prove that "determinism is incompatible with a number of a priori desirable assumptions".