 As with just about everything else in the foundations of quantum mechanics, there remains considerable controversy about what exactly Bell’s analysis demonstrates. (For further insight into the various controversies see Maudlin 2014 and Goldstein et al. 2011. See also the entry on  Bell’s Theorem.) Nonetheless, the opinion of Bell himself about what he showed is perfectly clear. See Norsen 2011 for a nice overview of Bell’s views on the matter.