[Aratlithiel]

I personally believe that none of the decision to claim the Ring was Frodo's. I think by this point he had been so beaten down and weakened by his journey, his wound, the sting and various other maladies that the proximity of the Ring to It's master finally overwhelmed him. Even as he speaks the words, Sam observes that it is with a voice that is not his own.

And I think the wording of the phrase has everything to do with the point. If you read any of the Christopher Tolkien's "The History of The Lord of the Rings," you will see where J. R. R. Tolkien wrote and re-wrote many passages in the book to make the intentions of his characters more clear. Sometimes it was simply a case of rearranging words in a sentence to reflect the nuance that he was trying to illustrate.

IF Tolkien was attempting to point out that Frodo had no real choice in the matter, I have no problem believing that the precise phrasing was intentional.