I've looked over the material and I hold no misconceptions on what occured.
The US Armies own War College's Strategic Studies Institute has a paper titled "The Lessons of History: The Chinese Liberation Army at 75" by Laurie Burkitt, Andrew Scobell and Larry M. Wortzel (pg. 335) citing that:
"The CIA had worked to develop a guerrilla effort in Tibet from the time of the Korean war, and India tacitly, and later between 1959 and 1962 more actively, supported this effort"
This is even acknowledged by Indian sources that confirm:
"India, in the late 50s and 60s with the help of the CIA aided the Tibetan rebellion, providing training facilities in India" (Indian Defence Review: Volume 23 [pg. 24])
During this period the Nehru government ran to the US begging for more:
"...aid, and economic assistance [which] grew substantially between 1959 and 1963. India also received about $60 million [$500 million in 2012 dollars] worth of military assistance from the United States, including aircraft and radar".
In the book "The False Dalai Lama: The Worst Dictator in the Modern World" by the International Shugden Community (pg. vii) those same Tibetan guerrilla fighters were later inducted into the Indian Armies Special Frontier Force to fight Pakistan in Bangladesh in 1971 as part of the Mukti Bahini terrorist organization which was created by India as confirmed by the "Indian Defence Review: Volume 23" (pg. 24) which states:
"RAW was given the task of gathering intelligence and undertaking covert missions, including pro-insurgency" and "the operation involved getting the [terrorists]... in East Pakistan (Now Bangladesh) together and training and arming them"
It's the same as the bullshit lie India peddles about being "non-aligned". The fact is that you were aligned with the USSR after signing the "Indo-Soviet Treaty of Friendship and Cooperation" in 1971 of which there are many articles signifying a clear alliance one in particular to note of would be Article IX which states:
Each High Contracting Party undertakes to abstain from providing any assistance to any third country that engages in armed conflict with the other Party. In the event of either being subjected to an attack or a threat thereof, the High Contracting Parties shall immediately enter into mutual consultations in order to remove such threat and to take appropriate effective measures to ensure peace and the security of their countries.
It's that agreement, signed just
four months prior to the Indian invasion in 1971 since it was aware it was not capable of achieving victory alone, that resulted in the USSR sending its navy (including nuclear submarines) to assist in the blockade of the Bay of Bengal as confirmed by
Russian naval commander Vladimir Kruglyakov: