Yes, and to drive home to jadrian a point I keep making: A and D could NEVER have interacted in the past because they NEVER existed in a common light cone. They were "born" too far apart! So now you have to modify the physics so that the lasers that created them (which are pulse matched) must contain the information needed to yield the correlations. But that means it is the pulse that does this (since other lasers won't be able to do this). The pulse doesn't contain enough information to cause that to happen. So now you need even more ad hoc hypotheses to make it all work out.
And this is just one setup.