Big Mystery: The Nine Rings of Power

[The Might]

Ok...I'm a little confused here, so if I am right
The whole question here is did the Nazgul still have the Rings or did Sauron hold the Rings during the War of the Ring?
Well, as stated in the UT, when Sauron sent the Nazgul on their errand towards the end of June 3018, he still held the Rings.

...being each utterly subservient to the ring that had enslaved him, which Sauron held ~ UT, Hunt for the Ring

But as is pointed out, they seem to have had the Rings with them when they travel to Eriador...which doesn't make any sense
I'm really confused now

Also, allow me to quote from the Letters:

I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive; they would have obeyed or feigned to obey any minor commands of his that did not interfere with their errand – laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills.

This letter deals with Frodo's 'failure' in the Sammath Naur and so, it clearly states that the Nazgul did not have their rings during the battle at the Black Gate, and so also probably not during the Siege of Minas Tirith (so much for the WK idea).

I think they never possesed the Rings during this whole time, and that they were always held by Sauron.
As far as what Frodo saw is concerned, I am not sure what to say