"Genghis Khan himself was technically not ethnic Han, but he and mainly his successors saw themselves as legitimate Chinese emperors by establishing the Yuan Dynasty."

I guess you can try to argue some kind of blood purity, but I suspect you'll find yourself in bad company rather quickly on that one...

China is unique in that their biggest acquisitions of land came from being conquered and then assimilating their conquerors (Mongol and Manchu).

It would be erroneous to say that later events retroactively made Genghis Khan Chinese.