The parent who is "also an OHSAA umpire" needs to crack open their rule book!
There is no such rule. A batter who receives ball four may overrun the bag. If the ball gets returned to the pitcher, the Look Back Rule can kick in, and there are some restrictions on what the runner can do at that point, but she is not automatically out for passing the bag.
Kind of scary to think that there's an umpire out there calling kids out for this perfectly legal baserunning move!
Since the NFHS now has their rule books on-line (you must be a registered official to access them), I can cut and paste the rule without doing a lot of typing! Note the part I have highlighted.
Rule 8-7-4 (When the Look Back Rule is in effect) Responsibilities of batter-runner after completing a turn at bat, and
while the pitcher has the ball within the 16-foot pitching circle, including a base
on balls or a dropped third strike are as follows:
a. A batter-runner who rounds first base toward second base may stop, but
then must immediately, without stopping, return to first or attempt to
advance to second base.
b. A batter-runner who overruns first base toward right field, turns left and
immediately stops, must then return non-stop to first or attempt to advance
to second base.
c. A batter-runner who overruns first base toward right field, turns left and
moves directly toward second base and stops is committed to second and
must attempt to advance non-stop to second base.
d. A batter-runner who overruns first base toward right field, turns left and
moves back toward the infield in any direction except directly toward second
base is committed to first and must return to first base.
e. A batter-runner who overruns first base toward right field, and turns right,
is committed to first base and must return to first base.
The rule specifically says that on a base on balls, the batter-runner may overrun the base. When the LBR is in effect, the runner must comply with requirements (a) through (e). When it is not on, the runner is not bound by any of these restrictions.
Next time you see this guy, amaze him with your superior rule knowledge by just casually throwing in that under rule 8-7-4 a batter-runner may legally overrun first base!