Tibet was part of the MONGOL empire, not the "Chinese" empire. And that was in ancient times. That is a dumb argument because in that case, Afghanistan should be part of India as should Pakistan. Balochistan should be part of Iran. All of the middle east should be part of Turkey. It goes on...
The fact is that China invaded and occupied it and systematically made the locals a minority.
They now used a clever trick to pretend to talk to the Dalai Lama and then just got up and left after the press reporters left. It's true that everyone looks out for their own interest but this was blatant tomfoolery and is not even in the Chinese interest since people can see they are not serious.