Runner hit with batted ball while ON a base.

[walkerbard]

Hi. I'm new to the forum. Need a ruling on this
situation that occured during a game. Situation:
infield back, runner on first gets hit with a
batted ball while ON the bag. Umpire calls
dead ball, BATTER OUT, runner safe (as opposed to
runner OFF bag where HE is out and batter is safe.)
The rule book clearly states that the RUNNER is
NEVER out if ON the base and ONLY mentions that
it will be a live or dead ball with regards to
the positioning of the fielders (in front of
runner/live ball, behind runner/dead ball) but
doesn't mention WHAT HAPPENS IF DECLARED A
DEAD BALL! Is it a HIT? Is the batter OUT,
runners return to bases? It doesn't mention
what becomes of the batter. Can anyone help?