Does a batter get first base if his batted ball hits the base umpire?

MLB Rule 5:09 states
The ball becomes dead and runners advance one base, or return to their bases, without liability to be put out, when --
...
(f) A fair ball touches a runner or an umpire on fair territory before it touches an infielder including the pitcher, or touches an umpire before it has passed an infielder other than the pitcher;
...
runners advance, if forced.
Since the batter becomes a base runner as soon as he hits the ball, this would mean he goes to first base. Although I admit I may be mis-reading Rule 5.09; you may wish to read it yourself.