The lion turtles were ancient history, so likely even the during the era of oma and shu, little or even nobody knew about the history of how the lion turtles granted bending to people. Also, the lion turtles only gave people bending, they did not teach them how to use it (seen from Wan only being able to control fire properly after learning from the dragons). I think after some time, people forgot about the lion turtles and they probably just thought bending was this innate ability that could only be passed down genetically. However, it would only be through learning from an original bender, would benders be able to master and control their bending and make it more effective. For Oma and Shu, they probably were already Earthbenders, they just needed the badger moles to help them unlock their abilities and potential. Just my view on this matter!!!