No it isn't. China under the Communist Party has never ruled or controlled Taiwan (since 1949). Taiwan democratized, developed, and got wealthy first, completely independently of China. Taiwan has never in modern history been an integral part of China.
Taiwan and China being one nation is the policy of the governments of both China and Taiwan.
Of course Taiwanese nationalism is it's own thing now, but the Taiwanese people seeing themselves as not Chinese is a relatively recent phenomenon - it's been functionally independent for less than 100 years, and before that it was a Japanese colony like several others that have since been reabsorbed by China.
I'm not supporting Chineses irredentism, and I don't think the parent comment was either. Taiwan should remain independent. What the parent was explaining is why China would want Taiwan no matter what - it's a historical part of China that is relatively recently separated, so they want it for purely nationalistic reasons. It's no different from Serbia and Kosovo, or Russia and swaths of Ukraine. The economics don't matter if all you care about is your wounded national pride.
No one in Taiwan and not even the current government consider China/Taiwan together. When KMT fled and created the constitution they claim China. Taiwan is now stuck in limbo because the people just want to live their lives in peace and already consider themselves Taiwanese and independent. But if they change the constitution then China will consider it a formal act of independence and use it as an excuse.