Coach2709 - maybe Matt or someone else will chime in with more knowledge, however the way I understood the rule, is if any defensive player (catcher) with a squeeze, or steal of home plate, steps on the plate, or crosses the plate - WITHOUT the ball in possession, constitutes a balk, not CI. CI only would come into play had the batter made contact with the catcher, then I think you are correct, batter gets first, and runner trying to steal goes back home, but without contact, I think you have a balk.
Since the balk was not called, I am still puzzled how the pitch being called a "ball" was not argued more, especially since the catcher clearly came out of the box to catch the ball. Looked like a strike to me, which would have ended the game if the missed balk call stood. Lot's going on!
7.07
If, with a runner on third base and trying to score by means of a squeeze play or a steal, the catcher or any other fielder steps on, or in front of home base without possession of the ball, or touches the batter or his bat, the pitcher shall be charged with a balk, the batter shall be awarded first base on the interference and the ball is dead.
Edit: looked at the 7.07 rule again, and looks like even if batter would have swung, then still a balk, and not CI...I think?