Yes, but what about what on happend on
Weathertop? The
Ringwraiths seemed to know exactly where they were.
On Weathertop
Frodo puts
the ring on his finger. That is what attracts the
Nazgul to him specifically. The Ringwraiths are enslaved, via their own
Rings of Power, to
the One Ring and to
Sauron. Sauron used the One Ring to enslave them. It's unsurprising that when a few feet from one activating the One Ring by donning it,. much as Sauron their master would do before losing the Ring, they would become aware of its presence.
Frodo isn't wearing the Ring when the Nazgul fails to detect him literally a foot or two away on the road which contradicts the notion that the Ring, absent being worn, attracts Ringwraiths. Likewise the Nazgul attack Crickhollow despite Frodo having departed days prior. They attack mattresses and pillows in
the Prancing Pony, and rely on human intel to track the
Hobbits to that
Inn, despite the fact that the hobbits aren't in the room they attack. Very clearly thay can't detect the Ring even if in very close proximity to it, unless someone is dumb enough to put it on their finger. And even then, the must be close to the wearer to be attracted to it. Frodo dons the Ring when he falls off the table in the common room, and no Nazgul materialize. It's much later after an
Easterling or even a half
orc sees Frodo's stunt and (
Tolkien makes a point) slips quickly out of the inn (to tattle to the Nazgul).