The Three weren't really bound to the One... except that they were made with the same technology (ringlore), and that the One was a master ring...
To CONTROL.

So... if we take the analogy of a computer... I am on a PII, when I log on the net, a more powerful computer (or just any old hacker) can take control of my machine, because his lore is deeper and stronger than mine...
BUT, when the master computer dies (or when the hacker goes off line), then my computer becomes free again, to roam wither it will.

Now, if we think about the Three and the One. The Three were never touched nor sullied by the hand of Sauron. His only control was that he was one heck of a hacker when it comes to Ringlore, so his One controlled all others, if they were worn openly...

So why should they fade with the passing of the One?? The hacker goes off to bed, so the Three, forged without the hand should not fade with him.
After all, the knowledge and Lore still exists. Why should something like the Three fade???

Makes no sense....

But hey, that's my rave for the day

Gandalf