I agree that the inclusion of the term "forward progress" is a bit confusing. Remember Rule 2-15-2 which defines "forward progress" for airborne players: "When an airborne player makes a catch, forward progress is the furthest point of advancement after he possesses the ball if contacted by a defender." We've always applied this before in situations not involving the sideline (receiver leaps and grabs ball at the 2, gets driven back to the 5, gets the ball at the 2).
Now we have the new definition of a catch which says if the player gets carried (implies "no longer under his own power") while in possession of the ball, you have a catch. So essentially if he's being carried he has completed the act of the catch and is thus a player in possession of a live ball, a.k.a. a runner.
So, like a runner, if he's taken backwards or straight sideways, then his furthest point of advancement is where he possesses the ball and begins being carried. Ball became dead in bounds, clock continues to roll. If he's taken forward, then his furthest point of advancement is determined once he crosses the sideline, clock stops.
It appears that the Fed's interpretation is that if the B player wants to extend the courtesy of carrying the A player further downfield inbounds, or even across the goal line, then Team A gets the benefit of that yardage.