The issue is much more complex than the main combatants, especially the Chinese government, would admit. The arguments circle around European concepts such as nations, states, borders, sovereignty, suzerainty, and so on, that weren't even invented, much less imported and accepted in Eastern Asia, until recently. To give a very short answer, there have been political struggles among Tibetans, Mongols, Manchus and other peoples for centuries on the Tibetan plain. The formal control over the Tibetan government has changed several times, but all this was more or less irrelevant for the common Tibetan, since the area has always had an extremely weak government, and every village, farmer's and nomad's clan more or less ruled themselves without interference from any kind of central authority. For a short period during the Yuan dynasty, Tibet was formally ruled by the Mongols that also ruled China. Then, during the Qing Dynasty (1644-1912) the Tibetan government again fell formally under Beijing rule, but again not under the Chinese, since they were then ruled by the Manchu. From the end of the 18th century, Manchu influence increased somewhat, and in the early 20 century they finally tried to make Tibet a more integral part of the Qing Empire. Merely one or two years later, though, the Qing Dynasty collapsed, China became a republic and Tibet announced its independence. Before this late Qing attempt to incorporate Tibet (around 1910), no Chinese ruler had ever imposed Chinese law, Chinese taxes, Chinese education, nor any other important cultural or political influence on Tibet, which is one of the reasons the Tibetans don't have any feeling whatsoever for having been ruled by China. Gradually, between the fall of Qing and the victory of Mao Zedong in 1949, the Chinese developed a nationalistic feeling (claiming to include the Chinese as well as the 55 "Chinese" minorities, among them Tibetans, Manchu and Mongols) and a reading of history where everything that had happened earlier in history was organically pointing to the Chinese nation of 56 peoples. Hence, the idea that even if the Mongols were not in any way connected to the Chinese in the times of Genghis Khan, they were still already "Chinese", since they were (i.e., would later become) one of the "Chinese" minorities. Thus, the huge empire of Genghis Khan was seen as a sign of the strength of the "Chinese". According to the same logic, Tibetans were defined as "Chinese", and thus everything that had happened in Tibet before the Chinese turned up became part of Chinese history. Seen in that way, it wasn't difficult to come to the conclusion that Tibet had always been and would always be Chinese, whether there were any relations to China and the Chinese or not. If the Tibetans ruled themselves, turned a deaf ear to Beijing and even threw out the Chinese official representatives (which they did after the fall of Qing), they were still never seen as a people of their own, but rather as a disobedient and troublesome child breaking off relations with his parents. However far you move, however independent life you live, you will never cease being your parents' child, and in the same way the Chinese started to see the Tibetans (and other minorities) during the first half of the 20th century: whatever they did and however independently they minded their own business without interference from China, they would never cease being "Chinese". Seen in that light, the invasion in 1950/51 was nothing other than restoring the order and bringing back the disobedient child to his parents. Needless to say, the Tibetans did (and do) not agree to this recently constructed interpretation of history.