I don't believe the rulebook is completely clear regarding this. So short of an "official" ruling, which I think in the end is what would really be needed, here's what I would say:
Since "Aid" is used to transfer to a companion or minion, but it doesn't specify where you transfer it from (Support Area verses another companion or minion). I would interpret that transferring is allowed. However, based on what is said on page 38, that the follower is borne by the companion for the rest of the turn; I wonder if that is just clarifying that the follower doesn't return to the support area during the regroup phase (or when the fellowship moves), but can still be transferred if something allows it to be. For example,
Sam, Bearer of Great Need can transfer a follower to the support area, even thought the default rule is for him to bear it for the rest of the turn.
In summary, in short of an "official" clarification, I would interpret that followers (Free Peoples and Shadow) can be transferred.