ASA's rules or interpretations never specifically addressed this scenario. For that matter, it STILL does not address a deflected fair batted ball leaving the field of play in fair territory!
Here is the difference as I see it. In the interpretation offered on the batted ball, there is no point where the defense ever controlled the ball, yet they caused the ball to leave the field of play.
In your scenario, the defense did possess and throw the ball, which is clearly covered in the rule book and has been for years. The rules specifically state that runners are awarded two bases from the time of the release of the throw. This award is not reset every time that thrown ball touches another defender even if that contact redirected or caused the ball to enter DBT.
The rules do address if the defender receives the ball and loses it attempting a tag, but that was not your scenario.