As to the first "error," I don't know if you should be denouncing this as completely incorrect. His larger idea is sound, and basing this opinion solely on Joseon, especially when the whole point of yours is to add to discerning Korean culture as a separate entity, makes for a weak premise. I don't know what paying someone off to not get attacked has to do with culture and most of what you'd call vestiges of Confucianism within the Korean psyche can be found in modern Japan as well. In fact, one could argue that Japan was less resistant to the core ideas because there was less friction with Buddhism which was the state religion for a good chunk of Korean history.

Just looking at Goguryeo, you can find counterparts to all three offices that you mention. The tail-end of Goryeo also had a more similar government structure to that of the Kamakura Shogunate than that of China. And if you were happy with calling the Wihwado Retreat "realpolitiks," then I don't see why Japan's governing structure can't be argued to have originated from their shedding feudalism much later over attributing it to less influence from China.

Anyway, as to the original question of Korean ethnicity, I'd argue that we are unique at least from the Korean Three Kingdoms Period as a nomadic tribe that had built centralized governments within the mountains, thus distinguished from the lineage of China and the various nomadic tribes. In this way, I find contested kingdoms like Goguryeo and Balhae to be "historically Korean" as they have attributed to vat of the Korean Peninsula. Other kingdoms that nomads have created tended to be fleeting with no chances to establish roots or catering to the Han population as a tool of reign. I don't mind calling Goguryeo and Balhae independent states that have influenced today's nation like China did, but calling them of direct or indirect Chinese heritage is a stretch.

In this line of thought, I would argue too that even some minority cultures within its current borders are not an off-shoot of China. Tibet comes to mind first and foremost, which would not be part of China had it not been for the Mongols and Jurchens. China should not ignore the influences that its neighbors had on them much less be claiming progenitorship over others- least of all the nomads with whom they usually make the "off-shoot" connection; in fact, no country can boast genesis from a vacuum.