The core tenant to not just Tibetan Buddhism but Buddhism as a whole is that of the middle way; a life of balance and understanding. Seeing as the majority of Tibet's population is in fact Buddhist it would only be logical to say that this is the favored approach of the Tibetan people.
No, the Dalai Lama's Middle Way is not the approach that people in Tibet favor, because the Dalai Lama is only trying to keep the peace. The Middle Way is simple a way of saying that no one is right. That might sound nice to the rest of the world, but it doesn't work for the people who have to live in the situation.