Good point Tom. IMHO fair or foul are used both to describe the location of and the status of the ball. The references used in Definitions, Rule 7-6, Rule 8-7 and Rules supplement # 23 only refer to the location of the ball at the time not its status. The quote from the umpire manual makes no sense to me but that’s not unusual (me not the manual). If the ball is legally caught the ball’s status is “live” and its location on either side of the line is irrelevant unless there may be some sort of scoring issue.
Another thought on the OP is that runners must be entitled to legally advance. If runners are obstructed during a foul ball they have to return as they cannot legally advance. A batter who runs on a 2nd strike uncaught who is obstructed must return and bat as they are not entitled to advance. A batter who is out on a fly ball is not entitled to advance and therefore cannot be obstructed.
Paul