Are non-Western University PhD's really frowned upon?
All degrees have value somewhere. What you need to think about is where you want to work when you complete your studies. Obviously if your goal is to work in Asia or particularly in Hong Kong there should be no problems with a Hong Kong degree.

Another concern to consider is whether you will work in academia or industry. Sometimes academia needs to hire people whose degrees are recognized by the local government. Sometimes for political reasons one country will not recognize another country's degrees unless the university is transcendently elite. This forces the university to look elsewhere for talent.

In industry, they usually do not need to hire people with degrees from government recognized countries.