I ask again, what is the primary source? Please cite it. The word rigs simply meant descent and its ancient usage is not the same as the modern concept of Minzu.Khampa always called themselves Bodrig. Bodrig literally means "Tibetan race" while Bodpa means " Tibetan". The reasons Khampas and Amdowas did not call themselves "Bodpa" was that "Bodpa" became synanmous with Utsang people. Even today there are few older khampas and Amdowas who doesnt use Bodpa to describe themselves because to their minds "Bodpa" is associated with Utsang people. In old days Bodrig meant all tibetans while Bodpa only meant Utsang people.
Both are under the indirect or direct control of the Gelukpa by the 18th century. The Bonpo tribes in Kham were forcibly converted to the Gelukpa under the Qing army during the Jinchuan wars. The entire Qing Empire promoted the Gelukpa order.Sumpa Khenpo Yeshe Peljor is a monk historian from the 18 century and his division of "Bodqen" Great Tibet and "Bodqung" little Tibet is intresting in the sense that Bodqung was under direct and indirect control of Gelugpas while Bodqen was not. Historiand I find Khempo Bodqen refers to Yarlung empire.
Most Amdo people I know today does not like using Lhasa as a common dialect among Tibetans. It is overseas Tibetans which seem to have settled in using Lhasa as the common medium.They are still doing it. Lhasa dialect is still shown as pristine and original while Khamke and amdoke is shown as rustic and backward. Even in local Kham and Amdo television Lhasa is shown as the standard for Tibetan.