The Seven and the Nine

[Alfirin]

That's true, unless Gandalf's inner maia fea lets him see the unseeable (I was never clear if beingswith a huge presence on the "spirit side" (like Glorfindel) could see other beings over there. About the only really poor evidence I can give for Gandalf knowing (or guessing) that the Nazgul aren't wearing their rings is something he DOESN'T do (or at least we are not told he does) When the burial team come to pick up theodens body and bury the slain fell beast, he doesn't tell anyone to try and keep an eye out for the WK's ring ( whether or not it was invisible while he was wearing it, it would presumably return to visibility with his demise). In his place, if I though the WK was wearing it, once circumstances allowed it, I might make a point of making sure it was in MY keeping, lest either some Mordor agent retrieve it and bring it back to the enemy who might have other "worthy" men just waiting (G does not know of the Mouth of Sauron, of course, but he probably assumes Sauron has more loyal men of evil waiting in the wings as need arises.) or some ususpecting Gondorian or Rhohirrim finding it, taking it as plunder putting it on, and falling into shadow (with Sauron so strong now, ring corruption might occur rapidly; rapidly enough to turn a man wraith in a short enough time to be a threat)
Speaking of plunder (and getting off topic for a sec). in an earlier thread I made mention of wondering if some Mordorian might have swooped down and collected the WK's iron crown to present it to Khamul (i.e. the new WK and Lord of the Nazgul) but it just occurred to me that, if this didn't happen, it is also well within possibility that the crown would be collected by one of the burial team. I imagine the crown and or cloak of the Witch King would be a SERIOUS battle trophy, whether for themselves, or to present to Eowyn. Unlike everything else, both of those items could be found, THEY are visible and since the WK got off his beast for the last battle, they aren't under its body.