I like Romanus's point. I think the idea that Ring could not be destroyed by any act of will sits well with the established power of the Ring. While that is aptly carried out in the book version where Gollum accidentally falls into the Fire, it is also carried out in the movies where, while wrestling for the Ring, both Frodo and Gollum fall off, but Frodo, in typical Hollywood fashion, manages to cling onto the edge. That is assuming we interpret the wrestling as Frodo trying to get back his Precious. In that regard, I guess the movie version does do it a bit better because it defeats an old cliche whereby the hero and villain have a climactic punch up at the end on a narrow walkway suspended over hazardous chemicals while maintaining their balance and not falling in, while the book version does seem a bit Carry On. "The Precious! The Precious! The Precious! The Precious! Oh bugger!"