As weird as it sounds the Republic of China on Taiwan currently claims to be the legitimate government of ALL of China.
What independence means is they give up this claim, actually, and just claim to be an independent island.
The Chicoms actually would be more POed by that than the decades-long claim that they were the legitimate government of the whole of China and that the Chicoms were an illegitimate government.
It might be so, but Taiwan itself is US territory even while the Nationalists are a Gov't in exile.