Welcome to active participation, Kboy!
The problem I have with your analysis is this...
The batter-runner
is not in violation of anything by running outside of the running lane. Runners, including BRs, are allowed to take any path to the base they darn well please.
But, they are not allowed to interfere with the defense (using the rule book definition of "interference"). For a thrown ball, there must be intent on the part of the runner. The only exception to this is the running lane violation, which deletes the requirement of intent, but leaves in place the definition of interference - that is, there must be a play. See Steve's definition of a play.
Merely throwing the ball to a defensive player standing at or near an awarded base is not a play.
Stating that a batter-runner is out if the batter-runner gets hit with the ball while out of the running lane absent any play is dodgeball. Even with a batted ball, merely getting hit with the throw while out of the running lane is not per se an out. The umpire must still judge there was a play (i.e. the BR was interfering with the fielder making the catch). Look for several old discussions on this topic using the phrase "quality catch."