That was Tolkien's clever trick for his rewrite - the "original" story was what Bilbo wrote down at the time (the "present") - the new edition was what was later edited in by Bilbo or Frodo as what really went down (after everything had been revealed in LotR.
I understand your claim. How do we know which explanation, or whether another explanation, is true?
Again, another strong explanation for the change in Bilbo's story: It was a demonstration of the corruption caused by the Ring and its effects on hobbits, an effect corroborated by Gollum's story about how Gollum acquired the Ring - all as explained by Gandalf.
