Hmm, might've spoken too hastily.
From the Comprehensive Rulebook:
"You may transfer an artifact or possession between your Free Peoples characters during your fellowship phase by paying the twilight cost for that artifact or possession again. (Minions cannot transfer artifacts or possessions.)
...
Transferring a card is not playing that card, even though you must pay its twilight cost. "When you play" game text is not performed when transferring a card."
I didn't remember the last paragraph being there; guess that takes it to a more general case, so you'd have to pay the twilight cost again for other card types as well.