"[Mount Doom] is...where [Frodo] will face the gravest challenge of all: the danger of physical and psychic ruin if he refuses to part with the Ring at the last moment."
This is true - the reader/audience waits for the moment, when Frodo is about to make the final decision. And, lo and behold, he chooses to keep the Ring for himself. Hopefully, I am undisputed so far. Gollum then makes his appearance after Sam looks especially sad, and then Frodo and Gollum wrestle about, and finally, both go off the edge, and Gollum falls into the fires of Mount Doom, leaving Frodo dangling. Here is what I wish to point out: Frodo never made the conscious decision to let the Ring go; he never chose to destroy it. Accident chose to sacrifice Gollum in the destruction of the Ring; it easily could have taken Frodo instead. They both wanted the Ring; Frodo fought with anger and greed, not righteous bravery.
The article talks about how "power cannot defeat power. Only the abandonment of power can truly defeat power. Might does not make right and never will." Frodo, however, did not abandon power. He wanted it just as Gollum did at those last moments - they became truly equal at the last moment. They truly became each other’s Shadows - doppelgangers - and one of them died.
Here is where I inevitably pull in the Heart of Darkness twist. In order for Frodo to overcome the Shadow he had hanging over - and leading - him through the entire journey, he had to let go of everything and become the Shadow itself. It then became a physical contest of power between Frodo and his Shadow.
I hope this was a good start. Ready, set, debate!