[Calacirya]

In a corny sort of way, I like to think that there was no involvement on behalf of the Valar, especially considering Gollum's trip over the edge in Sammath Naur.

I think that in some aspects Tolkien wanted to believe that bad things would come to bad people. In the Middle Earth universe, it can be argued that everything is very simple. Good people are good, bad people are bad, some people can change, and every once in a while there's a grey area.
I also believe he had this mindset because he always thought so fondly of the idea of Goodness, and it permeated his work. Frodo was the only one who could carry the ring because he was so good that he was not easily corrupted. Or at least, he was supposed to represent all that was good, as any soldier going to war for the right reasons.
Also, I believe it was a coping mechanism. It's easier to believe that good conquers all, even when all hope is lost, as it was in Sammath Naur when Gollum had the ring.

I suppose it could also be in the Music of the Ainur, as it did redound in the splendor of Eru's greater plan. I just like to think, and I think Tolkien, too, thought, that sometimes Good happens in this world.