You are only partially right......
The declaration of independence from 1913 became effective according to international law never from Chinese view, since it was ever recognized neither by China nor by any other state.
from wikipedia
".....Millions of files in both Chinese and Tibetan recording historical facts over more than seven centuries are being kept in the archives of Beijing, Nanjing and Lhasa. No government of any country in the world has ever recognized Tibet as an independent state.
British Foreign Secretary Lord Lansdowne, in a formal instruction he sent out in 1904, called Tibet "a province of the Chinese Empire." ....:"
from http://www.index-china.com/index-english/Tibet-s.html
The claims of both the People's Republic of China to Tibet, which are generally recognized by nations having diplomatic relations with the government, are based on the Qing Empire having exercised once suzerainty over Tibet and of never having renounced this authority. This is important to the Chinese governments because it establishes a history of rule over Tibet as well as providing a legal theory of Chinese rule of Tibet under international law, albeit one which is disputed by supporters of Tibetan independence.
That the Qing Empire once exercised suzerainty over Tibet is not in doubt: the Qing Empire occupied Tibet throughout the 18th century and signed treaties with Great Britain in which Britain recognized Chinese suzerainty over Tibet. However, a few pro-Tibetan independence supporters argue that suzerainty does not equate with sovereignty and that Tibet therefore should not be part of China.
also from wikipedia