[mbyron]

Thanks, Dave. I phrased my response as a question rather than assertion because I couldn't find anything definitive about the OP's play 1. As I read the rule, however, the principle seems to be to remove any advantage gained by the offense due to the actions of the improper batter, including advancing due to a walk. By the same token, the rule explicitly permits any advance due to the actions of the defense, such as a balk, wild pitch, etc.

The ambiguity in the rule concerns actions by the defense sufficient to advance the runner that occur after the batter's time at bat (and so not covered by the NOTE that Dave quotes). Since the BR is typically advancing at this time on a batted ball or a walk, do we invoke the principle denying advantage to the offense or allowing the defense to suffer the consequences of their mistake?

R1 advanced both due to the BB and the WP. Since either one would be sufficient to advance the runner, moving the runner back would not only being a denial of benefit from BOO but also an intervention in favor of the defense. I would allow the advance to stand.

Wish I had something authoritative, though. I looked through J/R's BOO cases (there's about 20), and didn't see anything perfectly apposite.