tifo, I don't remember a requirement that a theme had to have a negative... but reviewing the three in question, fidelity, perseverance and loyalty, I would say that Gollum, and Boromir (who thankfully repented), provide some antithesis to Sam's and Aragorn's loyalty and fidelity; and Denethor provides the opposite of perseverance: despair.
In addition, you could say that in the very end, poor Frodo, crushed and broken and at the end of all his reserves, falls himself into despair, faithlessness and even treason. Sam provides the antithesis for him, and Gollum is the (uncooperative) vehicle of grace by which Frodo's effort is redeemed.
So, in cnsidering your definition, I would still say that these are themes.
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...down to the water to see the elves dance and sing upon the midsummer's eve.
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