But they’re carrying shared quantum state — why would it be surprising their actions were correlated? Eg, that particle being a particular state is correlated

But they’re carrying shared quantum state — why would it be surprising their actions were correlated? Eg, that particle being a particular state is correlated to Alice picking a particular measurement because the total system must maintain that quantum number. The particle which emitted the photon and the particles which give way to Alice have carried that information since the inflationary period — and so the photon and Alice share that correlation now. The conclusion seems to be “the correlation must be at least this old!” — but that’s exactly the claim being made. So I’m not sure I understand the problem for Bohm-derived models.