The first problem has to do with the prominence "narratives" are currently given in the study of history. A legitamite method in literature and anthropology, the idea that history itself is simply a group of "narratives", none better than the next, and that there are no bona fide "facts" (or at least very few "facts"), has been festering in this field for some time. So much so, that "collective memory" and "cultural images" are now more discussed and studied than what actually happenned, when and why. Perhaps the prime example of such warped thinking is Mark LeVine's study of Jaffa, which if the promo is any indication, is more concerned with how people perceived their cities than with how things actually were.
This is not to say that perceptions of events do not have a place in the study of history. History, after all, is the study of human actions and thoughts, and these can't be understood without knowledge of the cultural background, and, yes, the "narratives" or ideas that run through various socities. We are not simply a collection of fact-collecting robots, always working according to some non-human rules regardless of where we come from. We are creatures of our surroundings, whether we reject or embrace them.
As imortant as "narratives" might be, however, their value stops at the door of the establishment of the factual record. The essential, critical part of history which examines what happenned, when and why, has no place for "narratives" or "multiple truths" or "rashomons". The fact that Israelis and Palestinians perceive the actions of Officer Hinks differently does not mean both, or even either, perception is correct. Officer Hinks may be a murderer (for killing a family in cold blood) or a hero (for killing rioters) or neither, but he can not be both. As Yoav Gelber points out in his important essay on history - either 80 or 250 people were killed at Tantura - both numbers can not be correct. History only happenned one way, and as much as Prof. Bar-On and Dr. Masalha would like to have Israelis and Palestinians listen to "each other's narrative", in many cases one, or both of the narratives will be false.
If history, especially charged history like the Arab-Israel conflict, is to remain a legitamite discipline and not a laughing stock where charlatans and story-tellers can claim equal standing with actual historians, the border seperating fact from perception or "narrative" must be clearly maintained.