Actually, that was David Crockett, of the Volunteers from Tennessee. Mr. Boone, while an honorable gentleman, was from Kentucky. There is no account of him killing a 3-year-old bear, of which I am aware.
I have no proof that Daniel Boone never killed a 3 year-old bear(or that he did, for that matter). Countless hours of research on the subject leaves the final conclusion unresolved.