Pet Theory about who Tom Bombadil is

[Inziladun]

I think I've actually heard that theory before, though I seem to remember it being presented in a joking fashion.

However, the indications are that the Witch-king, as all the Nazgûl, was completely conquered by his ring, and an extension of Sauron's will.
In the Unfinished Tales chapter The Hunt For the Ring, we are told:

At length [Sauron] resolved that no others would serve him in this case but his mightiest servants, the Ringwraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held.

(empahsis added)

Also,

.....if one of [the Nazgûl], even the Witch-king their captain, had seized the One Ring, he would have brought it back to his Master.

It seems clear there was no 'partial conquest' of the WK's will, allowing for inner debate. That was Gollum's problem.