http://www.folklore.ee/folklore/vol31/berezkin.pdf
This theory goes back over a 100 years:
"Its stars seem to have been called the Bear over nearly the whole of our continent when the first Europeans, of whom we have knowledge, arrived. They were known as far north as Point Barrow, as far east as Nova Scotia, as far west as the Pacific Coast, and as far south as the Pueblos."
- Stansbury Hagar, “The Celestial Bear”, The Journal of American Folklore (JAF), Apr.-Jun., 1900
"Occasional local names notwithstanding, the possibility of the bear as Ursa Major having originated independently is inconceivable. Classical Old World mythology is replete with the bear in its role as Ursa Major. Ancient Greek, Hebrew, and Arabic all contain references to this motif."
- William B. Gibbon, “Asiatic Parallels in North American Star Lore: Ursa Major”, JAF, Jul.-Sep., 1964.