It depends on how you look at the history and the peoples, so Trump is not wrong either.
No trump is completely wrong.
The modern korean state and its predecessors were never under any Chinese administration.
I have actually taken the time to read
internal court documents in both Joseon and Ming/Qing dynasties.
And you must understand the context here.
Before accepting the westphalian system of countries, China considered itself to be the Middle Kingdom, with the emperor as the son of heaven, who ruled over
all.
There was the concept of tianxia, "all under heaven," implying the authority of the dragon emperor over all domains of earth.
Would you then claim that every territory in the whole world was Chinese?
In fact, English were so desperate to trade with China, that they send the Mccartney mission, which happened in the form of a tribute to China.
Would you then claim that England was a part of China?
China did impose tributary relationship with almost all countries around China, but the ones with Korea and Vietnam is way deeper than that, those two actually adopted everything Chinese.
Not only those two. Even Japan, (and at that time Ryukyu)
In fact, there are very funny stories on all three fronts.
The concept of "Zhongguo" "Huaren" etc. was very flexible.
Let's talk about Korea.
Korea was an
officially Confucian state under the Joseon dynasty. It had deep reverence for the Ming Dynasty, which it copied profusely.
However, when the Manchus overthrew Ming, and formed the Qing. For some time, (a century to be exact), the Joseon refused internally to accept the Qing, as the Zhongguo. They called the Qing as barbarians internally, and derided them.
In fact for some time, Korean confucianists, started calling their own country as the Zhongguo, because they thought that the barbarians have pillaged everything good about the Celestial Kingdom, and Korea was the true inheritor of everything Chinese.
Similar, thing happened with Vietnam. Vietnamese routinely called themselves the Huaren, and in fact even labelled their country as Zhongguo for some time.
In fact they started calling the Cambodians, etc. the barbarians.