The idea that Rey came from "nothings" or "nobodies" is absolutely fucking fantastic and wonderful. The Prequels set aside the Force as the providence of the Jedi, of beings with a high midichlorian count. Everyone has the Force, but only people who have high midichlorians can actually be effective with it. Changing it instead so that saying that the Jedi have prevented people from using it by being the focus of a cult of personality, and shifting it to something which truly is in each of us, putting our responsibility back on us for looking out for ourselves, and taking action against oppression — that's beautiful.
Kylo missteps by announcing it in that fashion to Rey. He intends to hurt her enough to push her into his arms. Kylo is using a PUA technique by trying to get Rey to feel useless and alone, and only he understands her. It's fucking brilliant and chilling, and REY IS HAVING NONE OF IT.
At the same time, because she asks to see her parents and is instead shown an image of herself, it's also possible that she's another manifestation like Anakin, which would go some distance toward explaining her strength.