Why not, but as far as we know within the inner movie logic the saber goes to her, she does not take the saber.
How on earth do we know that? When have we ever seen an inanimate object leap into someone’s hand on its own? The saber “calls” to her earlier in a One Ring kind of way, but we have no reason to believe it can shoot itself across physical distances. You could make the argument that the saber chose between Rey and Kylo, but Rey still had to decide to go for it in the first place.