Now you're treading on dangerous ground! :)
You're explanation sounds as good as any. Apparently Tolkien meant for Bombadil to be a mysterious character but I hate it when they're this mysterious. To me, all these questions lead back to "Who or What is Tom Bombadil?"
OK, so here's a question for any Silmarillion readers. Is there any clue as to who or what Bombadil is in Iluvatur's Song of Creation?
It seems obvious Bombadil is similar to the pagan green man, or nature god. CS Lewis had a theory, which perhaps Tolkien shared, that where and when the pagan gods were real and forces for good, they were basically holy angels in disguise. The Valar are the angels of Middle Earth. Does the analogy hold? Is Bombadil a Valar?