Ball Thrown Out of Play after Infield Hit


 
With no runners on base, the batter (B1) hits a ground ball to the shortstop. The shortstop fields the ball but then drops the ball and does not make a throw to first. B1 arrives safely at first base, but B1 thought his ground ball went into the outfield, so after touching first base, he makes a wide turn into fair territory. 
 
When the shortstop sees B1's wide turn, he fires to ball toward first base. B1 runs back towards first base, but the throw is wild and goes out of play. Where does the umpire place B1?
 
A) First base, since B1 was heading back to that base at the time of the throw.
B) Second base, since the throw was the first play by an infielder -- B1 should be awarded two bases from the time of the pitch.
C) Third base, since B1 should be awarded two bases from the time of the throw.
 
Call
When the defense throws the ball out of play, it is a two base award (NF 8-3-3c). If every runner, including the batter-runner, had advanced one base, the award is from the time of the throw.
 
In the situation below, since the batter-runner had reached first base, he is awarded two bases from the time of the thrown -- placing him at third base (answer "C").