Does Bell's theorem rule out the possiblity that measurements are completely determined by events in the past light cone? I'm studying Bell's theorem and the CHSH inequality for some time. Now it's clear to me that one cannot reproduce the correlations predicted by quantum mechanics by assuming that particles carry hidden variables with them, and measurements depend only on them. 
But what about the case where we consider the most general scenario: the measurement outcome can depend on the entire past light cone. Why not? 
This would mean more information are available when the detector "chooses" an outcome, than just the variables carried by the current particle: for example the measurement of the current particle can depend on previous measurements, past measurements on the other detector when they reached the past light cone of the current event, etc. 
Is it possible to show that such assumptions are also ruled out Bell's theorem? 
 A: Yes, as long as you're assuming a local hidden variables theory it can be shown that even allowing the outcome to be determined by any arbitrary amount of prior events in the past light cone will not allow for violations of Bell inequalities. Bell demonstrates this for example in his paper "La nouvelle cuisine" which is reprinted in the collection Speakable and Unspeakable in Quantum Mechanics. For a free online paper that discusses how you can include entire cross-sections of the past light cone in proofs of Bell's theorem, see "J.S. Bell's Concept of Local Causality"--note in particular Fig. 1 and Fig. 2 on page 4 of the paper, and the way equation (1) on that page defines the locality condition using the complete set of "beables" (all local variables, whether measurable or hidden variables) $B_3$ in a cross-section of the past light cone (region 3 in Fig. 2).
A: Yes, Bell's theorem (together with the Einstein-Podolsky-Rosen argument) necessarily implies that causality is nonlocal, i.e. causal connections outside the past light cone exist.  So the past light cone is not sufficient to determine all measurements.
Note that this is regardless of whether hidden variables exist or not.  This is an often-misunderstood point.  It's not, "Choose your poison: either hidden variables exist and causality is nonlocal, or hidden variables do not exist and causality is local."  It's, "Causality is nonlocal. Period."
(Note, BTW, that your statement in the first paragraph is not true:  you CAN reproduce QM correlations with a hidden variable theory, but that theory will be nonlocal.  David Bohm invented pilot wave theory to demonstrate that a hidden variable theory is capable of reproducing QM correlations.)
The logic is like this:  EPR says, in effect, "If QM is true, and causality is local, then hidden variables exist."  Bell's theorem says, "If hidden variables exist, and causality is local, then QM is false."  If the experiments demonstrate "QM is true" (as most people think they do), then those syllogisms become:  1.(EPR) If causality is local, then hidden variables exist.  2. (Bell) Either hidden variables do not exist, or causality is nonlocal.  Combining those: if causality is local, then (by EPR) hidden variables exist, so (by Bell) causality is nonlocal (contradiction).      
