The extended probability ensemble decoherent histories (EPE-DH) interpretation of quantum mechanics proposed by Murray Gell-Mann and James Hartle posits that there is one real fine-grained history of any quantum system. More specifically, they postulate that, in the sum-over-histories treatment of quantum mechanics, one of the histories is actually real. They make this postulate consistent with predictions of quantum mechanics by employing extended probabilities (which can report probabilities greater than one or less than zero). According to this interpretation, quantum mechanics is a local theory.
My question: If this interpretation posits locality, how does it account for interaction free measurement?
For example, in the double-slit experiment, and according to this interpretation, any particle that makes it to the detector screen behind the slits only passes through one slit or the other, even if no detector is present at the slits. This means, after multiple runs, there are histories of particles passing through slit 1, and histories of particles passing through slit 2. But if I close slit 1 before I start the experiment, two things happen: There will be no histories where the particles pass through slit 1 (understandable), and the histories of particles passing through slit 2 will be altered (if this was not the case, interference patterns would presumably persist).
I don't understand how this interpretation accounts for the alteration of the histories of particles passing through slit 2.