Well... Tom is supposed to be the eldist (older than the hills etc.) the witch king certainly is not. He was born in the second age. Also, the witch king is invisible, Tom is not. Also, the witch king is a slave to his ring (one of the nine) which in turn can be controled by the one ring, thus I doubt that the ring would have no affect on him. Also, Elrond and Gandalf had both heard of Tom (Elrond also spoke of knowing him from past ages, and also mentioned his age), so I think this theory is pretty far fetched.
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