Tibet and Mongolia has been Chinese territory for hundreds of years from 17th century onwards. Tibet's socalled brief independence was instigated by British colonists in India, to pre-empt the Russians annexing Tibet. It was a power game between British and Russia to exert their influence to profit on the juicy China trade, while the weakened China was powerless to do anything.
Russians were aggresively grapping territory after territory in Far East and Central Asia, It was greedy and eyeing for lands in Mongolia, Xinjiang and Tibet. The British colonists under British East India Company, having conquered India sub-continent as trophyin their bag could never accept Russian controlled Tibet next door to their power base in South Asia. China had been defeated battles after battles with British, French, Japanese in may wars (Opium wars, sea batlles of Dalian, Fujian, Vietnam border etc) and 8 nations expediction forces in Boxer incidents, they could not stop the scheme of British East India Company's plan.
The "independence" was never recognised by the government in power then, i.e. Republic of China, and its successor, the People's Republic of China. Thus PLA's re-taking of Tibet was legitimate.
More-over the so-called "traditional cutural value of old Tibet" is one hell of appalling society comprisng of Priest-gods, warlord/land owners, soldiers, and slaves. Dalai Lama was the "living buddha" cum the ruler (which is a big contrast and against teachings of the historical Buddha who gave up his throne and kingdom, and lived among the common people.) The warlords/land owners and their soldiers treated the slaves with-out mercy because their doctrine that slaves were born to be what they are and deserved to be teated as such due to their past Karma. It was a kind of caste systems, childrens of slaves became slaves automatically and their whole lives belong to their lords.
Majority of Tibetans in exiled are mainly from the ruling class (lamas and slave owners) and their servants and soldiers who were oppresived against poor Tibetan slaves.