Are you sure you're not Cory from Cali? (eteamz reference...)
ASA does have problems from time to time with a difference between the literal reading of a rule/exception/note and what is intended. Think of it this way. 8-7-P is about runners who are not runners. They could have achieved that status by either scoring, being put out, or by being a batter. Second, the exception about BR running on the third strike rule should actually say a batter or retired batter running as if it were a dropped third strike. That is what ASA intends here.
Regardless, you will not find a rule about a batter running to draw a throw, except in this exception.