Back then the US was already in the thick of its anti-communist, anti-Soviet global Cold War and needed China (the Kuomintang regime) as an ally. That is why it officially recognized China's sovereignty over Tibet. However, Washington was not comfortable at all with the Tibetan dilemma, as it really wanted the vast resource-rich region in its own pocket.
In 1949, the US consulate in Hong Kong issued visas to members of a "Tibetan business delegation" without Kuomintang's consent and brought them to America to engage in "Tibet independence" activities. The separatist, theocratic elites in Tibet joined the conspiracy by launching an "oust the Han people" campaign as a step toward splitting China. The US media also played its part by propagating that "the US is ready to recognize Tibet as an independent and free country".
In June, 1950, the outbreak of the Korean War finalized the US policy of "helping Chiang (Kai-shek) against the Communist Party" and "using Tibet against the Communist Party of China". The China containment strategy featuring limited military aid for Tibetan separatists and containing China with covert warfare thus became the basic characteristic of Washington's Tibet policy. As a result, Tibet in Southwest China and Taiwan in the country's southeast stood out with their geo-strategic significance as two key pieces in the China-containment section of the US Cold War strategy, while the issue of Tibet became a "favorite subject" of the Cold War.
In the early 1950s when the People's Liberation Army (PLA) marched into Lhasa and liberated Tibet peacefully, the US government encouraged and supported the separatists in Tibet to obstruct the liberation of Tibet with armed resistance.
In 1951, the Truman administration tried to persuade the Dalai Lama to flee abroad in the hope of making him a political factor in its anti-China campaign overseas. In 1956, US agents from the Central Intelligence Agency (CIA) promised support for Tibet's independence in their talks with Tibetan separatists. And in March, 1959, Washington instigated the separatist forces in Tibet to launch an armed rebellion and helped the Dalai group rebuild its military arm known literally as the Four Rivers and Six Ranges Religious Guards" (Sishui liugang weijiaojun), while funding the formation of the "Indo-Tibet Special Frontier Force" by India and the Dalai group. These armed forces then launched numerous attacks in China's border areas against the PLA troops stationed there as well as against civilians.
It should be noted that the US National Security Committee and the State Department were responsible for making Tibet-related policies, while the CIA executed them. These included specific actions in its secret war against China, "spearheading" all conspiracies to abet and help the Dalai group in its separatist attempts.