Was Gollum's slip the only way?

Though it is not entirely clear what the power was that cast Gollum into the fires of doom, there was definitely some great power at work. Gollum attacked Frodo and Sam on the side of Mount Doom. They could have killed him there, but showed him mercy. There is a paragraph that has describes Sam's view of the scene. He see's Frodo as a tall figure in white clutching at the ring under his shirt. Frodo tells Gollum that if he ever touches him again, he shall be cast into the fires of doom. I believe it is the power of the ring itself that binds the curse and becomes the source of its own destruction when it is in Gollums posession at the time he is cast into the fires of doom. NOTE: I have read The Lord of the Rings several times over the years and it was only in my most recent reading that I realized this relationship.