Sure, the other players probably should have been paying attention and said something, but it's tough to argue that this is more "fair" than the option I suggested. There are certainly arguments against it (added complication, different rules for ball 1 than the rest of the game), but it's tough to argue that it's not more "fair" than the other option. I personally think it's worth the added complication to make thinks more fair. I also think it logically makes more sense have the affected player play on a game starting with 0 score, maintain original play order, and not deal with a compensation ball. I don't have any data to back it up, but my guess would also be that playing out of order is most common on ball 1 (in games with extra balls off).
Pinburgh finals and the game is on Monster Bash. P1 is playing, P2 and P4 are sitting in the chairs off stage, and P3 is sitting on stage. P1 finishes his ball and starts walking off stage. P2 starts walking up the ramp to play her ball, but while she is doing so P3 starts playing. P3 isn't able to trap up and allow P2 to take control, so P2 gets a compensation ball. P3 is DQ'd. The players remaining in the game all play pretty well. P2 ends up draining ball 3 (her second ball) with Monster Bash lit. After P4 finishes play, she ends up 20M or so behind each of the other players before her compensation ball. She starts the compensation ball with no progress and is unable to catch the other players. This ends up being the difference in who advances in the round.
In this scenario, P2 ends up screwed through no fault of her own. Obviously, this happens all the time in pinball, but usually there is no simple way to fix it. In this case, however, there is. I think that it's worth some added complication to address this.