This story sounds doubtful to me. It's perfectly OK for a Chinese to say that they are from Taiwan, and Chinese, be it from the mainland or Taiwan, always say that: They're from Taiwan, Beijing, Guangdong, you name it. It's like saying which state you're from in the US.

No-one ever says "Chinese Taipei", certainly not among Chinese, which is just some political compromise, mostly in the Olympic Committee.

The only issue I can think of is if the question was specifically about the country of origin, in which case some people may indeed object to "Taiwan" and argue that it should be "China" instead (but not "Chinese Taipei"...)