Catcher's interference

[UMP25]

But it sounds like in his scenario that R3 didn't "steal"; rather, he advanced to home as a result of the passed ball.

I'm surprised that no one mentioned the fact that on catcher's interference, it's a delayed dead ball where if the batter-runner and all base runners advance a base, then said interference is disregarded. Here, the B-R swung for strike 3, the ball got away for a "dropped third strike," and R3 scored as a result. Disregard the interference and let the play stand: R3 scores and B-R is at first.