The PRC says that Formosa (i.e Taiwan) is part of China. That's why I added the caveat (for some definition of China). There are political definitions, cultural definitions, linguistic/anthropological definitions. So, my statement still stands that Taiwan is a kind of China, depending on how you understand that word.
It's clear that you're speaking from a political perspective, but even that gets a bit grey.
Since you don't live in China, you should know that there are hundreds of different versions of China within China itself. You could live in Shanghai and never know the reality of the China that the people of Xinjiang experience. So I would say to your points that:
1) The markets all over China are very different.
2) The talent pools all over China are very different.
If YC wants to call it YC Shangjing, (because they're primarily targeting those two markets), that would be fair. But considering China just to be Shanghai and Beijing is a bit myopic, which is why I suggested Taiwan in the first place.
Disclosure: I am a Chinese-American currently living in Northwest China, which is VERY different than Shanghai, Beijing, Guangzhou, Shenzhen, Linxia, Shenyang, etc. all of which I've visited.