Direct quote from page 365 of the Del Rey Paperback of the Silmarillion:
"For Frodo the halfling, it is said, at the bidding of Mithrandir took upon himself the burden, and alone with his servant he passed through peril and darkness and came at last in Sauron's despite even to Mount Doom; and there in the Fire where it was wrought he cast the Great Ring of Power, and so at last it was unmade and its evil consumed."
The bold is mine. Obviously, the true story is only known to some. It would also not reflect well on Frodo for everyone to know that at the last, he claimed the ring for himself and would have doomed the world if not for Gollum's last act of desperation, so perhaps this distortion in the 'official record' can be forgiven. Also, he took the burden of his own volition, not "at the bidding of Mithrandir."