There is a problem with that theory. 90% of Brahmaputara's water came from territory south of Himalayas, only 10% of the water comes from Tibet. Same with Indus river. Vast majority of water originate south of Himalayan mountains, not from the north. North of the mountain (Tibet) is a desert and even the most of the glacier flow originates from the southern slope of the mountain. In the north of the mountain, annual rainfall is less than 400mm, while south of the mountain, it's 3,000mm, contributing to much of the glacier formations and water flow. Ie, even though Tibet is 40% catchment area for Brahmaputra, most of the water comes from wetter southern slope of Himalayas (India). Read more here (
https://www.preventionweb.net/news/choking-brahmaputras-flow-much-ado-about-nothing )
Even if China dams entire water, it won't have any significant effect. India can always dam brahmaputra ( and screw Bangladesh) to make up for any reduction in water flow.