Chinese cities are very safe in general, in terms of safety you can almost compare them with HK, Seoul and Taipei. (perhaps with the exception of Shenzhen, where the population are majority migrants who could disappear without trace -- it is perhaps the single incidence where your finger-cutting story comes from. in fact the only similar story i heard of happened in HK about 10 years ago, where the lady was killed and the robbers have been stalking her for many days about that huge diamond ring.).
i see no problem wearing jewelry on the street, esp in broad daylight and in tourist areas where there are a lot of people. (but then all streets in china are packed with people
)
if she has a gweilo next to her. she is a lot safer. because the potential thief/robber knows that if they mess with gweilo they would attract more attention from police
in my hundreds of trips into chinese cities, i often walk on streets even in the middle of the night. never ever saw a single robbery.