Actually I think it implies that Tom wasn't given to interfering with other beings unless they were actually causing trouble or in danger. As long as the Barrow Wights didn't have anyone to bother, he left them to their own devices.
If that is the case GB it supports the theory that he would have aided the Dunedain- who were in danger. And the Witch-King definitely counts as causing trouble.
I think it does too. As long as the Witch-king kept to himself, Tom wouldn't have bothered with him at all. But because he was out to cause trouble in the region under Tom's beneficence, I think Tom would have been forced to step up in some manner.