...What you say may be so, but it only works for Bilbo and Gollum. The
essential issue remains an issue. We could simply ask the same question
again only replace "Bilbo" with "Frodo." Your reasoning explains the
differences in Bilbo and Gollum's stories with respect to the Ring, but Frodo
possessed it, too, and his story diverges from Gollum's as much as
Bilbo's. And at that point in crafting his story Tolkien presumably knew
what sort of story he was telling and what sort of power the Ring had. In
the end, the first explanation (given by NZ Strider and an seileachan) becomes
necessary.