[Arestelwen]

You're right Orual, Boromir did want the ring from the beggining. But I think he was meant to go as well as Frodo was meant to carry the ring.
Consider that Boromir's attitude made Frodo decide to go alone at the end.

But back to the question, I think Frodo knew somehow that he had to take the ring. Of course the ring was "calling" for him, and he didn't want to leave it, but he was in a really unconfortable position. Like when someone asks who did something and everyone knows it was you, but noone says anything. Someone else that didn't have to take the task was going to take it if he didn't speak.
It was a noble thing to do.