

Sorry, I still don't buy it.  You're certainly right that the runner is
not out merely for running out of the baseline: he must interfere with
the play.  But the argument here is over what constitutes interference.
You certainly cannot infer from what you've quoted that the batter-runner
must be hit by the ball to be guilty of interference: you haven't posted
a definition of interference at all.

IMO this calls for one of the "approved ruling[s]" that go in small print
in the rulebook.  Something like:

APPROVED RULING:
If in the judgement of the umpire the runner, by running to the left
of the allowed path, caused the fielder to make a bad throw, blocks the
vision of the fielder receiving the throw, or otherwise impedes the
defensive team's making a play on him, the batter-runner shall be
judeged guilty of interference.

or

APPROVED RULING:
The runner cannot be judged guilty of interference in the unless he makes
contact with a fielder or is hit by the thrown ball.

--
In the absence of such an approved ruling I claim that this is a poor
rules trivia question--since it cannot be authoritatively answered.