Tagging a Runner While Injured

 
The runner on 2nd base (R2) is stealing on the pitch. The batter hits a ground ball to the shortstop, who fires the ball toward 3rd base to try to retire the advancing R2. The ball and the runner arrive at 3rd base at the same time, but the hard throw hits R2 in the back of the neck. R2 falls down, is tagged by the 3rd baseman while off the base, and is obviously injured. 

Is R2 out on this play (he was tagged off the base) or does he remain at 3rd base (after all, the defense's throw caused R2 to lose contact with the base)?

Call
Unless (in the judgment of the umpire) the shortstop intentionally attempted to injure the runner, then the runner is out when the ball is live and the runner is tagged while off the base.

I got into some "spirited" discussions on when to call "time" when a player is injured.

"Time" should not be called/granted until the conclusion of continuous playing action -- UNLESS -- continuing the play would further risk injury of a player.