Runner Placement after overturned out call

HS varsity.  Runners on 2nd and 3rd two outs.  Batter hits ball to second.  The throw is bad and the 1st baseman has to dive up the line to grab it, he is off the bag but has the ball.  Batter/Runner touches the bag while the defender is on his back.  BU calls the BR out at first.  Both runners cross the plate, runner from second was about 20 feet from the plate when the out call was made  and the 1st baseman was still on his back.  Offensive coach comes out and asks BU to check with the Plate umpire.  They converse and the BU changes the call to safe, so still 2outs and runner at 1st.  Defensive coach comes out to talk to PU and PU puts the runner back to 3rd.  So my questions is why is the runner placed at 3rd?  No play was attempted but the 1st baseman.  What rule/mechanism was applied to substantiate the placement of the runner at 2nd back to 3rd base? 

HS varsity.  Runners on 2nd and 3rd two outs.  Batter hits ball to second.  The throw is bad and the 1st baseman has to dive up the line to grab it, he is off the bag but has the ball.  Batter/Runner touches the bag while the defender is on his back.  BU calls the BR out at first.  Both runners cross the plate, runner from second was about 20 feet from the plate when the out call was made  and the 1st baseman was still on his back.  Offensive coach comes out and asks BU to check with the Plate umpire.  They converse and the BU changes the call to safe, so still 2outs and runner at 1st.  Defensive coach comes out to talk to PU and PU puts the runner back to 3rd.  So my questions is why is the runner placed at 3rd?  No play was attempted but the 1st baseman.  What rule/mechanism was applied to substantiate the placement of the runner at 2nd back to 3rd base? 

Swampboy:  Thanks for the explanation, but without any attempt at a play by the 1st baseman and where R2 was at the time of the call I thought it was odd that they sent him back to 3rd.  I can see why the defensive coach would argue for that.