I still think, there are a lot more evidence of the Tibet becoming a protectorate under the the Qing Dynasty, from the Qing appointing an Amban to take care of Tibet to stationing a garrison in Lhasa.
Many times there are conflicts in Tibet the Qing were on hand to assist and driver off invaders.
The Ganden Sumtseling Monastery was first established by the 5th Dalai Lama, later the Emperor Kang Xi completed the construction of this grand monastery.
So plenty of older evidences to support China's claim on Tibet.