It's a little more complicated than that.
I went through the history of Tibet on Wikipedia, and zoned out about halfway through. The reader is welcome to sort it out for themselves.
Suffice it to say that its historical sovereignity is the same dog's breakfast as it is for Europe, the Middle East, and much of the rest of the planet. There are damn few countries on Earth that can't be claimed as somebody else's territory at one time or another.