Tibetan Buddhism believes Dalai Lama is the highest level of living Buddha. Thus the tradition is that they follow it. If Dalai is in China, no Tibetans will be in poor/dirty India. In fact, many run-away Tibetans are disappointed with Dalai group after being there for many years, they want to leave there and go back to their home Tibet, but they can't, as they can't prove they are Chinese due to lack of documents. They get stuck in a land of misery.
They have government in exile in India because the slave owners don't like communists abolish their dark, ugly theocratic serfdom. They found their commonality with Indian caste system, and they love to see India still maintain that inhuman system in effect. They thus moved into India like greenhead flies moving onto a pile of stinky sh!t of animal.