Tolkien's implication is that this is why the Host of the West is able to fairly easily defeat Melkor/Morgoth at the end of the First Age. He has sunk so much of his power into controlling Middle EArth that he has little left to fight the attacking Host.
Maybe Tom B has gone the other direction. His originally much lesser power is so highly concentrated that it is able to resist even the power of the Ring.
Also, I see his resistance to the Ring as not one of power so much as one of attitude. He just doesn't care about what the Ring can tempt him with.
I seem to remember Gandalf, in describing his unsuitability as an ally, saying that ultimately Bombadil would fall to Sauron as Sauron is able to torture even the earth. This seems to imply at least a connection with the earth itself.