In my opinion, i think the Woman with the Grey hair is actually Tigraine: or more precisely, Moridins mother. I think as the barriers weakend, the DO pulled Moridin and Tigraine from the multi-verse: one where Tigraine ignored Gitana Moroso and stayed to have Galads younger brother instead of heading to the Aiel waste. With Rand and Moridin being the opposite sides of the same coin... then think on it for a moment: if the DO was to beat you, then would it be the most sinister if he beat you, with you? Or more precisely, who Rand would have been if different choices had of been made.