Be careful about how this is stated. It can be interpreted two ways - one is a myth and the other isn't.

Last I saw in FED rules, if a batter-runner reaches first on a BB and overruns the base he can be legally tagged out. He is only entitled to the base.

That said, a BB is still a live ball and a runner can run past first base and try for second in an attempt to draw a throw.

No big deal as long as whoever reads it interprets it the same way as the person who wrote it.