Let me just say this.
This whole idea that people see themselves as a combined racial identity like White people or Asian people is not exclusive everywhere. Maybe That's normal in US where the average person can be several different ethnicities but still under one racial umbrella. Maybe even Asian Americans think of themselves as a collective ethnicity of Asian but in Asia we don't. We see each other as distinct groups of people with our own pluses and minuses.
We also understand that insults against Asians by Westerners are primarily targeted at the Chinese so insults against the Asian people by non-Asians tend to be Chinese related like go back to China, ching chong, chingy, herro preeze etc. so that if somebody start making comments about Chinese towards you It can be interpreted as racist and I don't think you can disagree that the granny didn't like Chinese/Asian people and her remark was intended to be racist, such that being Chinese was the insult and as I'm not Chinese I found it even more insulting but it would have been insulting if I were Chinese in that context as well. There are just so many negative stereotypes about Chinese that being called Chinese has become an insult.