It was 4 months after the 5S released.The genius wouldn't know. There is nothing on the white box phones to identify if they're new or refurb. The only way that he would have a good CHANCE of being right, is if your phone was replaced within the first couple months of the release date of your phone. Even then, those could be refurbished as well.
I guess I have no way of 100% knowing if it was new or not, I am basing it off of the fact that the genius bar said it was new. He even said it was like his third iPhone 5S taken into the genius bar at this certain store ever...Anything in a white box is a refurb......but some people like to think otherwise. Refurbs are ok, not new but still ok.