There is one, and only one, applicable rule to examine when deciding if the batter gets an RBI--Rule (a)(3).
10.04 Runs Batted In
A run batted in is a statistic credited to a batter whose action at bat causes one or more runs to score, as set forth in this Rule 10.04.
(a) The official scorer shall credit the batter with a run batted in for every run that scores
(1) unaided by an error and as part of a play begun by the batter's safe hit (including the batter’s home run), sacrifice bunt, sacrifice fly, infield out or fielder's choice, unless Rule 10.04(b) applies; NOT APPLICABLE.
(2) by reason of the batter becoming a runner with the bases full (because of a base on balls, an award of first base for being touched by a pitched ball or for interference or obstruction); or NOT APPLICABLE.
(3) when, before two are out, an error is made on a play on which a runner from third base ordinarily would score.
(b) The official scorer shall not credit a run batted in
(1) when the batter grounds into a force double play or a reverse-force double play; or NOT APPLICABLE.
(2) when a fielder is charged with an error because the fielder muffs a throw at first base that would have completed a force double play. NOT APPLICABLE.
(c) The official scorer's judgment must determine whether a run batted in shall be credited for a run that scores when a fielder holds the ball or throws to a wrong base. Ordinarily, if the runner keeps going, the official scorer should credit a run batted in; if the runner stops and takes off again when the runner notices the misplay, the official scorer should credit the run as scored on a fielder's choice. NOT APPLICABLE.
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The scorer's only job when deciding whether or not an RBI should be awarded is to consider what would have happened if the ball had been fielded cleanly, in reference to Rule (a)(3). If the runner on third base "ordinarily would score" on the play, and RBI is awarded. If not, no RBI is awarded.
So, let's go through the possibilities of what would have happened if the ball had been fielded cleanly, and the consequences:
A) Fielder throws to second, forcing the runner. The SS may or may not have thrown to first, but that is irrelevant here. Either way, the run scores.
B) Fielder throws to second, but runner beats the throw. The run scores.
C) Fielder throws to first, throwing out the batter/runner. The run scores.
D) Fielder throws to first, batter/runner beats the throw. The run scores.
E) Fielder throws home, forces runner at the plate. The run does not score.
F) Fielder throws home, runner beats the throw. The run scores
G) Fielder throws to third, the runner may or not beat the throw. The run scores.
H) Fielder, for whatever reason, is unable to get a throw off to any base. The run scores.
Reiterate the fundamental fact: the only way not to credit an RBI is to show that the runner "ordinarily would NOT score," i.e., to show that choice E above is the most likely, or at least very likely outcome of the play. There is no other way not to credit an RBI. Period.
Given the fact that all we know is that the IF was at double-play depth, choice E seems quite unreasonable as the likely outcome. That is why the correct choice is an RBI, and is why WIS changed it.