Maybe because of the Quinghai province that is the origin of the Yangzi Jiang, the Huang He and the Lancang Jiang, know usually as the "Three rivers" !
It's all about water as elsewhere! "What can I do, What can I write, Against the fall of Night". A.E. Housman
Mind you, it's ironic that China's contribution to global warming is melting the very glaciers that feed the rivers, rendering the ownership futile. keep to the Fen Causeway
The difference in definition is a major source of dispute. The distribution of Amdo and eastern Kham into surrounding provinces was initiated by the Yongzheng Emperor during the 18th century and has been continuously maintained by successive Chinese governments. Tibetan exiles, in turn, consider the maintenance of this arrangement from the 18th century as part of a divide-and-rule policy.[citation needed]
But then I'm no expert on hydrology of that scale :-) "What can I do, What can I write, Against the fall of Night". A.E. Housman
It can't help that the province of Amdo is where the Dalai Lama comes from...
Amdo was and is the home of many important Tibetan Buddhist monk scholars or lamas who had a major influence on both politics and religious development of Tibet including the 14th Dalai Lama, the 10th Panchen Lama, and the great reformer Je Tsongkhapa. It was traditionally a place of great learning and scholarship and contains many great monasteries including Kumbum Jampa Ling (Chin. Ta'er Si) near Xining, Qutan Si and Labrang Tashi Khyil south of Lanzhou.
In 1751, the Manchurian (Qing) government, which ruled China between from 1644 to 1912, established the Dalai Lama as both the spiritual leader and political leader of Tibet who lead a government (Kashag) with four Kalöns in it.[3] Between the 17th century and 1959, the Dalai Lama and his regents were the predominant political power administering religious and administrative authority[2] over large parts of Tibet from the traditional capital Lhasa.