We know from Azys Lla that the Allag were experimenting on dragon-based chimera and we know from the Lore book that by the end they were also experimenting on the spoken races. Their scientists had unfettered access to Tiamat as a sample and they may have also had access to Bahamut's corpse.

The Au Ra may be in the same situation as the Ixali - they're descended from chimerical Allagan creations, they just don't know it, and what they do remember is filtered down through thousands of years of oral history.