This is addressed in the article:

"Now, in his conversation with Frodo, Bombadil implies (but avoids directly stating) that he had heard of their coming from Farmer Maggot and from Gildor’s elves (both of whom Frodo had recently described). But that also makes no sense. Maggot lives west of the Brandywine, remained there when Frodo left, and never even knew that Frodo would be leaving the Shire. And if Elrond knows nothing of Bombadil, how can he be a friend of Gildor’s?

What do we know about Tom Bombadil? He lies."

The only word we have is Bombadil's. Not that I buy this interpretation, but your complaint is addressed there.