You've proven my point for me.
You can't match someone who's Japanese with someone who's Chinese as easily as you would someone who is Japanese. That is because "asian" describes phenotypic traits, not ethnographic heritage. People who's families and ancestors reside in a geographically similar area have more of a chance of being related somehow. That is why I use the phrase "ethnic group" rather than race.
When it comes to something as sensitive as transplants;putting an organ into someone that needs to function, I can imagine a high levelof genetic similarity is required, and sometimes even that doesn't work and people die. Its a very risky medical procedure that requires a huge amount of care and precision. That makes sense.
However, in study groups it had been observed that there are extreme generic similarities between people from different corners of the globe. Sometimes individuals will find that they are genetically more similar to someone from another ethnic group than the ethnic group they are descended from.
I also know for a fact that transplants between people from different ethnic groups DO happen. My cousin received a kidney from his black friend. Our whole family is Swedish American. However I'm not an industry expert on transplants; just Anthropology, so the extent of my knowledge is limited to my experience.