Another thing to consider would perhaps be who saw it at the Council - Merry, Pippin and Sam did not, and neither Merry nor Pippin saw the Ring at all. (Save for the one time Merry saw Bilbo use it to escape the S-B's) Frodo, in the face of all gathered, actually said that it should go to Aragorn.
Quote:
'Then it belongs to you, and not to me at all!' cried Frodo in amazement, springing to his feet, as if he expected the Ring to be demanded at once.
'It does not belong to either of us,' said Aragorn, 'but it has been ordained that you should hold it for a while.'
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(emphasis mine)
Why should he expect that? Did he learn something of the nature of Strider while travelling with him?