In the end what we think is immaterial. The point is that Tolkien thought that this world is one in which we have the freedom to choose our actions and that we are personally responsible for them. For Tolkien, each decision really does come down to a moral choice for good or ill, and without that structure his mythology and his novels make no sense. Moreover it would be extremely odd for a Christian to believe that we are simply automatons performing predetermined actions in a random and meaningless universe.
However we might view the primary world, Tolkien's sub-created universe is one with a creator, a supreme being who is the source of good. This benificent presence gives meaning to Tolkien's universe, and the presence of evil within that universe introduces the necessity for moral choice and individual moral responsibility. Many of the workings of Arda make no sense whatsoever when divorced from this structure. Now, the supreme being may sometimes intervene, directly or indirectly, but Tolkien always forces his characters to decide their own actions for themselves.
In the case of Frodo, we do actually have Tolkien's word for it that he could never have resisted the temptation of the Ring in the final crisis. Thus the conclusion of his quest presents a moral lesson about his tolerance and mercy toward Gollum. If Frodo and Sam had killed him, as it was only logical and sensible to do, then he would have been unable through his final treachery to save Frodo from the domination of the Ring. Essentially, Frodo has the opportunity to decide whether he is to destroy the Ring and complete his mission or to claim it as his own and be destroyed, but his will has been overcome. He is no longer able to make the decision for himself, but the outcome of his earlier decisions has been to bring the means of his salvation with him. All in all this does not overturn the basic premise that Frodo possesses free will within the context of Tolkien's fiction (which is the only context in which he exists in any case). Perhaps someone who has access to their books will be able to give the location of Tolkien's reflections in his published letters.
Before I was sidetracked down this philosophical path, I meant to point out that the Eagles as a
deus ex machina were also discussed in
Flaws in Lord of the Rings... Yes in the book., which is also still open. There were some nice reflections there from Kalimac among others. There's also a thread called
The Great Eagle Mystery, which immediately sprang to mind when I saw this discussion. These may be of help on this matter, and I certainly make more valuable contributions in the former thread than I have here. If you wanted the lyrics to albums by the Eagles, you should look at
this site.