IMHO, many people are interpreting this 'death' as an actual, physical death, and I don't believe that's the way it will happen. The prophetic statement regarding Logain was not him stepping over Rand's grave, it was him stepping over Rand's body, but the body appeared hollow and crumbled away (a faked death perhaps?). I truly believe that Rand (with Alivia's help) will somehow fake his death...and that his faked death will be integral to Logain's 'Glory to come' as viewed by Min.
But that's just my opinion. I could be wrong. ;)
Perhaps Logain kills the person pretending to be Rand. Before Faile killed the profit he thought about how the "Dragon" came to him and told him Perrin is a darkfriend I think perhaps one of the forsaken is the person who spoke to him.