Before I continue, for the record, I just wanna repeat that I think followers probably weren't INTENDED to go from one companion to another.
But that doesn't mean I won't keep arguing that point, 'cause, hey... I like arguing. =P
I think it's possible that the line from the rulebook ("The follower is borne by the companion for the rest of the turn, no matter how often your fellowship moves") could just be telling the player that there's no built-in mechanic that sends the Follower back to the support area. So, in other words, it could just as easily say, "Unless either player does something about it, the Follower will continue being borne by the companion for the rest of the turn, no matter how often your fellowship moves."
And we know there are things that a player CAN do to prevent that from happening -- they could use
Sam, BoGN to transfer a Follower back to the support area, or the Shadow player could discard the Follower with
Ill News is an Ill Guest, or whatever. And, similarly, they could just pay the aid cost and transfer again, because there's nothing in the rulebook saying you can't transfer from one companion to another, or that you can't transfer an already-transferred Follower.
Once again, just playing devil's advocate here, but I think it's entirely possible that the line in question could be interpreted to mean, "This is what happens to Followers on a double-move if the players leave them alone. But, obviously, there are things that can be done to them."