I picture the scene - after Frodo's wound is taken care of (Elrond finds the
splinter and withdraws it), Frodo's wound is dressed by either Elrond or an Elf
nurse. Frodo is then dressed, probably by an attendant AND Sam, and Sam is
given a chain to put the Ring on and place around Frodo's neck. I don't think
Sam would bother mentioning it because to him it would simply be part of caring
for Frodo and dressing him. Is he going to say he dressed Frodo? Probably not.
Why should
he?
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"[In the book] You meet Faramir (Boromir's brother) and he's like joshing with Frodo about the ring and he says 'I wouldn't take this thing if it lay by the wayside, nothing could induce me to pick this up ...' which on first glance is a great line but dramatically, you can't go there. So that was all about deepening the choices and the journeys that these characters have to go on. And for a guy like David Wenham (Faramir), who is a very potent and powerful actor, you know where this story is going with him and we're setting up his character, but we wanted him to earn that moment when he sets Frodo free. It's gotta be a dramatic moment, it can't be this little conversation piece around a fireside. What happens to Faramir for releasing Frodo, sets up his character for film three and this plays a huge role in it." - Philippa Boyens