PetroGuy, I think you are wrong on this point. Check MLB rule 10.12(d)(3). The official scorer shall not charge an error against any fielder who makes a wild throw in attempting to complete a double play or triple play, unless such wild throw enables any runner to advance beyond the base such runner would have reached had the throw not been wild;
One of the point of scoring errors is to account for the runners' advance around the bases. There are no extra bases to account for in this situation. The batter is safe at first because of the fielder's choice. If the fielder had only made the play at first, the runner going to second would be advanced by the batter putting the ball in play. There is one exception mentioned for the First baseman.
Rule 10.12(d) Comment: When a fielder muffs a thrown ball that, if held, would have completed a double play or triple play, the official scorer shall charge an error to the fielder who drops the ball and credit an assist to the fielder who made the throw.
but that assumes a good throw, which was not the case in this situation.