Welcome to the 'Downs, solikat!
The two verses (poems) you quoted are actually an example not of fate but of prophecy. And they both came true.
I think what Tolkien is insinuating in LotR is not fate but rather the devine hand of Iluvitar (the Middle-earth version of God). It's been mentioned elsewhere around the board that Iluvitar had a lot of sway in the events of the War of the Ring, though we never learn his name until "The Silmarilion".
That's just my two cents.
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WWAHD? (What would a Hobbit do?)
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