Fascinating. I lack Steven Coblert's Tolkien lore recall, but had this head-canon: since Gollum spied on Frodo & Sam so long, Gollum knew everything they did.
OTOH I don't remember if Gandalf told Frodo about the other rings😬
I see now my unforced error was bringing up Gollum at all, as it exposed I score poorly on Tolkien portion of Nerd Credibility test.
But I got a good joke:As a frequent #OpenSource event-goer, I am annoyed most event organizers don't seem to know about Second Breakfast.