Yes, the Dalai Lama's middle way approach in Tibet is supported internationally, because the Dalai Lama is extremely popular. The Dalai Lama is not only respected worldwide, but he is revered. His approach to peace has been successful and has been a good way to find a middle ground in Tibet.
It should not be because they are just making things worse in that region by trying to find any excuse they can come up with to prolong the whole situation just because they do not want to accept China as there government. They should just count their blessings and be grateful.