This is patently not true. There are plenty of Chinese in the previous generation that gave up their hukou/ID card as required when they gained permanent residency in another country, and use their passport internally (when returning to work in China) like us foreigners must (it seems like these days it isn't necessary to turn in your hukou, but it was in the 90s). A previous colleague at MSRA was in this boat. It was troublesome for sure, but he could fly (even a Chinese can fly internally with a passport, as my wife did when we went from BJ to GZ), open bank accounts (like foreigners can), and so on. The only thing I know he had trouble with was permission to visit Taiwan, they couldn't handle a Chinese citizen without hukou, but that was it.
I'm as critical of the Chinese government as anyone, but bad information really doesn't help.