[The Might]

I disagree.
While the giants are actually there, and their existence is proven, for me these were-worms are only a hobbit myth, and you probably know how good they are at making up stories.
However, behind the story of the were-worms there might be some truth after all. We are told that cold drakes still survived in the northern wastelands, so it could be that Hobbits knew of their existence under then name of were-worms.