You want her to call herself 新加坡人???
Then (again), a lot of Singaporeans will say she is insincere.... 'come here few years then say she is Singaporean' etc. It's just too damn difficult to please Singaporeans, you know.
She is from Beijing. Nothing wrong.
Hokkien lesson:
唐山 = Deng Suah
唐人 = Deng Lang
Ask an elderly Hokkien speakers... Deng Lang = Chinese.
And YET, 唐山 is in China, near Beijing.
If you are a Chinese born in Singapore. Any Hokkien speaker, when asked about your race would say, he is 唐人 = Deng Lang = Native of Deng Suah.
You are so far from Beijing and you are Deng Lang... so I don't see nothing wrong with Jiawei saying she is a native of Beijing.
Long after you migrate (if you choose to one day when you find that to be a postman you need a degree here), when asked about the place of your birth, you are going to say, I was born in Singapore. Or you may even call yourself a Singaporean.
Most people are proud of their own countries (once an American, always an American, once a Chinese, always a Chinese), unlike Singaporeans (until someone points out something disparaging about Singapore) who are very quick to call themselves 'Australian', 'UK Citizen', or 'I'm American' barely months after getting the green card just because they married some ugly white guy who cannot even find a girlfriend back in the USA - sporting a fake accent, of course!