Listen to this logic.So just because every nation, empire, kingdom are NOT of a single ethnicity means you can just claim their achievements as chinese? If there was an tibetan king who ruled all of china, would that be chinese achievements or tibetan achievements?
Well, your argument against that Mughals were Indians or that Yuan was Chinese IS that they are not the same ethnicity.
Since not every nation on this world is a single ethnicity, your argument is invalid; there could be empires that span over several ethnicity and can claim several lineage. Austrian Hungarian Empire, for example, can claim two distinctive heritage - Austrian, and Hungarian. England, on the other hand, can claim several - Walsh, Scottish, Anglo-Saxon, etc. The great conqueror, William, who is French, landed on England, conquered England, and was proclaimed the king of England. Is William, and thus his heir, English? Cato the Censor, perhaps one of the more famous bonni, was not Roman in his youth, but became one of the greatest Roman in history, is Cato not Roman because of his birth, or his Italian background? When the Macedonian Pharaohs ruled over Egypt, can you say that these are Greeks, and not Egyptians?
Just because in your narrow mind, that one must be either or, does not make it so in history. Numerous man can claim several lineage, just because you cannot accept such an idea does not make them invalid.
Mughals can be BOTH Persians and Indians, and Yuan can be both Mongols and Chinese.
And according to the laws of PRC, yes, the Tibetans can claim the achievement of China, as they are citizen of China, making your points further ignorant.