The only answer we've been given on "when does Fallout 4 take place" is "200 years" after the bombs fall. Which is most likely an approximation, since Bethesda historically has always wanted to move forward on the timeline (to the point where they asked Obsidian to put New Vegas after 3, instead of before). I don't think people should take the 200 years line that literally and start acting like it's a fact.