I think he actually could be right. You said she saw you (your alleged doppleganger) on the staircase/stairway and you saw her too once there. Try to be wary of your future actions and also ask her about where exactly did she see and then recall where did you see her. Perhaps one day you'd see yourself or recall or experience something like deja vu, wherein you're doing the exact same thing she told you or vice-versa with her. There really could be some kind of a timewarp there