Did the batter just stand at home throughout the whole play?
Anyone who has read my posts, knows that I am not a proponent of MSU, and try to apply the rules as written. When I said "fairest" it is acknowledging that both teams did something wrong: The defense threw to second when there was no possibility of an out there, and the offense created contact with the catcher during that ill-advised throw (Note that I am not calling it interference).
IMO
1. The batter-runner has no 'right' to first while interfering with the defense. After ball 4, she is no different that a runner from 1st to 2nd and cannot get in the way of the defense making their play.
2. It is really hard to tell from a textual description, but the umpire has to take intent into account*. If the runner deliberately tried to get in the way of the catcher, then interference is likely appropriate. In most ball 4 calls, the runner takes a second to listen for affirmation before dropping her bat and then running. I'd be really interested to see how that batter handles ball 4 without any runners on.
3. Technically, it is illegal for the catcher to throw to any player except the pitcher unless a play on a runner. In this case, you could argue that the catcher was wrong (although as other's commented that is a strerch too far)
End of the story, I think TMIB is right - the catcher made a throw that was not an attempted out - no interference. Sounds like a little bit of a trick play by the offense which the defense fell for.
*- One training video this year showed a RH batter trying to bunt with the runner at first was trying to steal. The bunter stumbled into the area in front of home plate and disrupted the catcher's throw. It looks innocuous until they show you the previous pitch/bunt attempt where the batter doesn't get close to getting in the throwing lane.