[Amanaduial the archer]

I think when it says Sauron posseses the rings, its means that he owns them rather than has them with him. The nazgul are the kings whose downfall was brought about by the rings and I think the rings are what allows Sauron to so colsely control them. Also this is the reason why they can sense the one ring and even more strongly so when one puts it on- the nine are linked to the One.